Results_MachineLearning.txt

[
    {
        "videoId": "rKsjlA4fEeW7HSIACy8Jxg",
        "questions": []
    },
    {
        "videoId": "Iq7-fL1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "6Ypr1hQ-EeeFZBJX5mIoyg",
        "questions": [
            {
                "id": "yeEoMxykEeeKxgq5rEPplg",
                "type": "checkbox",
                "definition": "<text>\"A computer program is said to learn from experience E with respect to some task T and some performance measure P, if its performance on T, as measured by P, improves with experience E.\" </text><text>Suppose your email program watches which emails you do or do not mark as spam, and based on that learns how to better filter spam. What is the task T in this setting? </text>",
                "options": [
                    {
                        "id": "0.3217165089626439",
                        "content": "<text>Classify emails as spam or not spam.</text>"
                    },
                    {
                        "id": "0.6127126640150993",
                        "content": "<text>Watching you label emails as spam or not spam.</text>"
                    },
                    {
                        "id": "0.7664927352929847",
                        "content": "<text>The number (or fraction) of emails correctly classified as spam/not spam.</text>"
                    },
                    {
                        "id": "0.7069224238394478",
                        "content": "<text>None of the above, this is not a machine learning algorithm.</text>"
                    }
                ],
                "answer": [
                    "0.3217165089626439"
                ],
                "explanation": "",
                "videoCuePoint": 194881
            }
        ]
    },
    {
        "videoId": "IrD6Tb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "k0H3UrLrEeSTXyIACzQGuw@4",
                "type": "mcq",
                "definition": "<text>You\u2019re running a company, and you want to develop learning algorithms to address each of two problems. Problem 1:You have a large inventory of identical items.  You want to predict how many of these items will sell over the next 3 months.</text><text>Problem 2: You\u2019d like software to examine individual customer accounts, and for each account decide if it has been hacked/compromised. Should you treat these as classification or as regression problems?</text>",
                "options": [
                    {
                        "id": "1lRSp9xhCZ",
                        "content": "<text>Treat both as classification problems.</text>"
                    },
                    {
                        "id": "r7ZB9oOBve",
                        "content": "<text>Treat problem 1 as a classification problem, problem 2 as a regression problem.</text>"
                    },
                    {
                        "id": "bo9UzgFN2T",
                        "content": "<text>Treat problem 1 as a regression problem, problem 2 as a classification problem.</text>"
                    },
                    {
                        "id": "7wigrtDhe6",
                        "content": "<text>Treat both as regression problems.</text>"
                    }
                ],
                "answer": [
                    "bo9UzgFN2T"
                ],
                "explanation": "",
                "videoCuePoint": 678500
            }
        ]
    },
    {
        "videoId": "IrFvfr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "DIsCI26ARr",
                "type": "checkbox",
                "definition": "<text>Of the following examples, which would you address using an unsupervised learning algorithm?  (Check all that apply.)</text>",
                "options": [
                    {
                        "id": "5sSZfbyH6N",
                        "content": "<text>Given email labeled as spam/not spam, learn a spam filter.</text>"
                    },
                    {
                        "id": "cIrwuamv01",
                        "content": "<text>Given a set of news articles found on the web, group them into sets of articles about the same stories.</text>"
                    },
                    {
                        "id": "2gBgxGj2NR",
                        "content": "<text>Given a database of customer data, automatically discover market segments and group customers into different market segments.</text>"
                    },
                    {
                        "id": "hg80Rm7BvA",
                        "content": "<text>Given a dataset of patients diagnosed as either having diabetes or not, learn to classify new patients as having diabetes or not.</text>"
                    }
                ],
                "answer": [
                    "cIrwuamv01",
                    "2gBgxGj2NR"
                ],
                "explanation": "",
                "videoCuePoint": 780500
            }
        ]
    },
    {
        "videoId": "IrILv71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "MPky4kp4xX",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider the training set shown below. $$(x^{(i)}, y^{(i)})$$ is the $$i^{th}$$ training example. What is $$y^{(3)}$$?</text><table rows=\"6\" columns=\"2\"><tr><td><text hasMath=\"true\">Size in feet$$^2$$ ($$x$$)</text></td><td><text hasMath=\"true\">Price ($) in 1000's ($$y$$)</text></td></tr><tr><td><text>2104</text></td><td><text>460</text></td></tr><tr><td><text>1416</text></td><td><text>232</text></td></tr><tr><td><text>1534</text></td><td><text>315</text></td></tr><tr><td><text>852</text></td><td><text>178</text></td></tr><tr><td><text>...</text></td><td><text>...</text></td></tr></table>",
                "options": [
                    {
                        "id": "CEgT77LLCl",
                        "content": "<text>1416</text>"
                    },
                    {
                        "id": "VsZTBP5GWA",
                        "content": "<text>1534</text>"
                    },
                    {
                        "id": "muEi5gyrg3",
                        "content": "<text>315</text>"
                    },
                    {
                        "id": "YfU9ilgrvJ",
                        "content": "<text>0</text>"
                    }
                ],
                "answer": [
                    "muEi5gyrg3"
                ],
                "explanation": "",
                "videoCuePoint": 278500
            }
        ]
    },
    {
        "videoId": "IrNrUL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "kszH0bLrEeSTXyIACzQGuw@2",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider the plot below of $$h_\\theta(x) = \\theta_0 + \\theta_1x$$. What are $$\\theta_0$$ and $$\\theta_1$$?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/2.2-quiz-1-fig.jpg\" alt=\"A line of $$h_\\theta(x)$$ as a function of $$x$$. The line goes through points (0, 0.5), (1, 1.5), and (2, 2.5).\" />",
                "options": [
                    {
                        "id": "CEgT77LLCl",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 0, \\theta_1 = 1$$</text>"
                    },
                    {
                        "id": "VsZTBP5GWA",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 0.5, \\theta_1 = 1$$</text>"
                    },
                    {
                        "id": "muEi5gyrg3",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 1, \\theta_1 = 0.5$$</text>"
                    },
                    {
                        "id": "YfU9ilgrvJ",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 1, \\theta_1 = 1$$</text>"
                    }
                ],
                "answer": [
                    "VsZTBP5GWA"
                ],
                "explanation": "",
                "videoCuePoint": 132500
            }
        ]
    },
    {
        "videoId": "IrPggb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "d8Rtc7LCHS",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose we have a training set with m=3 examples, plotted below.  Our hypothesis representation is $$h_\\theta(x) = \\theta_1x$$, with parameter $$\\theta_1$$. The cost function $$J(\\theta_1)$$ is $$J(\\theta_1) = \\frac{1}{2m} \\sum^m_{i=1} (h_\\theta (x^{(i)}) - y^{(i)})^2$$. What is $$J(0)$$?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/2.3-quiz-1-fig.jpg\" alt=\"A plot of $$h_\\theta(x)$$ versus $$x$$. There are three markers on the plot: one at (1,1), one at (2,2), and one at (3,3).\" />",
                "options": [
                    {
                        "id": "9JcoJAKXH6",
                        "content": "<text>0</text>"
                    },
                    {
                        "id": "wEKo9vutSr",
                        "content": "<text>1/6</text>"
                    },
                    {
                        "id": "ZE1NZI8S5d",
                        "content": "<text>1</text>"
                    },
                    {
                        "id": "AuddBmY8xZ",
                        "content": "<text>14/6</text>"
                    }
                ],
                "answer": [
                    "AuddBmY8xZ"
                ],
                "explanation": "",
                "videoCuePoint": 412400
            }
        ]
    },
    {
        "videoId": "IrRVsr1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IrbGtb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "nzOSLZkEXV",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose $$\\theta_0= 1, \\theta_1= 2$$, and we simultaneously update $$\\theta_0$$ and $$\\theta_1$$ using the rule:$$\\theta_j := \\theta_j + \\sqrt{\\theta_0 \\theta_1}$$ (for j = 0 and j=1) What are the resulting values of $$\\theta_0$$ and $$\\theta_1$$?</text>",
                "options": [
                    {
                        "id": "TMhzXrsOre",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 1, \\theta_1 =2 $$</text>"
                    },
                    {
                        "id": "BdkbTkQkTo",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 1+\\sqrt{2}, \\theta_1 =2 + \\sqrt{2} $$</text>"
                    },
                    {
                        "id": "H0XLv3ka1X",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 2 + \\sqrt{2}, \\theta_1 =1 + \\sqrt{2}$$</text>"
                    },
                    {
                        "id": "AAyxg9FE2u",
                        "content": "<text hasMath=\"true\">$$\\theta_0 = 1+\\sqrt{2}, \\theta_1 =2 + \\sqrt{(1 + \\sqrt{2})\\cdot 2} $$</text>"
                    }
                ],
                "answer": [
                    "BdkbTkQkTo"
                ],
                "explanation": "",
                "videoCuePoint": 648000
            }
        ]
    },
    {
        "videoId": "IrZRhL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "F7CFqgWAOd",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose $$\\theta_1$$ is at a local optimum of $$J(\\theta_1)$$, such as shown in the figure. </text><text hasMath=\"true\">What will one step of gradient descent $$\\theta_1 := \\theta_1 -\\alpha \\frac{d}{d \\theta_1} J(\\theta_1)$$ do?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/2.6-quiz-1-fig.jpg\" alt=\"A plot of $$J(\\theta)$$ versus $$\\theta$$. The plot has a local minimum at $$\\theta_1$$.\" />",
                "options": [
                    {
                        "id": "fM2bYlhWSR",
                        "content": "<text hasMath=\"true\">Leave $$\\theta_1$$ unchanged</text>"
                    },
                    {
                        "id": "3NAsEMcLCo",
                        "content": "<text hasMath=\"true\">Change $$\\theta_1$$ in a random direction</text>"
                    },
                    {
                        "id": "6nZkhj8Aue",
                        "content": "<text hasMath=\"true\">Move $$\\theta_1$$ in the direction of the global minimum of $$J(\\theta_1)$$</text>"
                    },
                    {
                        "id": "dWYsa1K4Gg",
                        "content": "<text hasMath=\"true\">Decrease $$\\theta_1$$</text>"
                    }
                ],
                "answer": [
                    "fM2bYlhWSR"
                ],
                "explanation": "",
                "videoCuePoint": 484500
            }
        ]
    },
    {
        "videoId": "IrXcU71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "qC8kiV3NhH",
                "type": "checkbox",
                "definition": "<text>Which of the following are true statements? Select all that apply.</text>",
                "options": [
                    {
                        "id": "ywbT93ti2F",
                        "content": "<text hasMath=\"true\">To make gradient descent converge, we must slowly decrease $$\\alpha$$ over time.</text>"
                    },
                    {
                        "id": "WT9Kka8vqB",
                        "content": "<text hasMath=\"true\">Gradient descent is guaranteed to find the global minimum for any function $$J(\\theta_0, \\theta_1)$$.</text>"
                    },
                    {
                        "id": "J3dZndsMLr",
                        "content": "<text hasMath=\"true\">Gradient descent can converge even if $$\\alpha$$ is kept fixed. (But $$\\alpha$$ cannot be too large, or else it may fail to converge.)</text>"
                    },
                    {
                        "id": "s2jYX64VJX",
                        "content": "<text hasMath=\"true\">For the specific choice of cost function $$J(\\theta_0, \\theta_1)$$ used in linear regression, there are no local optima (other than the global optimum).</text>"
                    }
                ],
                "answer": [
                    "J3dZndsMLr",
                    "s2jYX64VJX"
                ],
                "explanation": "",
                "videoCuePoint": 544400
            }
        ]
    },
    {
        "videoId": "Irh0Zr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "3c2b16ed68c0fc61df870ea549d79271",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Let A be a matrix shown below. $$A_{32}$$ is one of the elements of this matrix.</text><text hasMath=\"true\">$$A = \\begin{bmatrix} 85 &amp; 76 &amp; 66 &amp; 5 \\\\ 94 &amp; 75 &amp; 18 &amp; 28 \\\\ 68 &amp; 40 &amp; 71 &amp; 5 \\end{bmatrix}$$</text><text hasMath=\"true\">What is the value of $$A_{32}$$?</text><text /><text />",
                "options": [
                    {
                        "id": "c81f138372906ce22c9b251b8012c5fb",
                        "content": "<text>18</text>"
                    },
                    {
                        "id": "ba095338b51acde90514e9cf92cb9fda",
                        "content": "<text>28</text>"
                    },
                    {
                        "id": "251e3a5ac86dff237f3cf96d5ecf2f05",
                        "content": "<text>76</text>"
                    },
                    {
                        "id": "0694c7e583da06ae47f839a1cd717150",
                        "content": "<text>40</text>"
                    }
                ],
                "answer": [
                    "0694c7e583da06ae47f839a1cd717150"
                ],
                "explanation": "",
                "videoCuePoint": 295300
            },
            {
                "id": "57859454cf35d425bd94006afdc9e1fe",
                "type": "checkbox",
                "definition": "<text>Which of the following statements are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "c1fb1b8b50ba0ea1b81af04fbae9fd54",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 1 &amp; 2 \\\\ 4 &amp; 0 \\\\ 0 &amp; 1 \\end{bmatrix}$$ is a $$3\\times2$$ matrix.</text>"
                    },
                    {
                        "id": "3d1f8157059753badbc389215f504601",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 0 &amp; 1 &amp; 4 &amp; 2 \\\\ 3 &amp; 4 &amp; 0 &amp; 9\\end{bmatrix}$$ is a $$4\\times2$$ matrix.</text>"
                    },
                    {
                        "id": "099686611ea7bb7ea009434f215604e4",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 0 &amp; 4 &amp; 2 \\\\ 3 &amp; 4 &amp; 9 \\\\ 5 &amp; -1 &amp; 0 \\end{bmatrix}$$ is a $$3\\times3$$ matrix.</text>"
                    },
                    {
                        "id": "f0c8f3b4195f2937ac4a3f3b82fe1e4d",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}1 &amp; 2\\end{bmatrix}$$ is a $$1\\times2$$ matrix.</text>"
                    }
                ],
                "answer": [
                    "c1fb1b8b50ba0ea1b81af04fbae9fd54",
                    "099686611ea7bb7ea009434f215604e4",
                    "f0c8f3b4195f2937ac4a3f3b82fe1e4d"
                ],
                "explanation": "",
                "videoCuePoint": 146300
            }
        ]
    },
    {
        "videoId": "Irjpl71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "969fd508d737a44cd4a5fe69a583942f",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">What is $$\\begin{bmatrix}4 \\\\ 6 \\\\ 7\\end{bmatrix} / 2 - 3\\begin{bmatrix}2 \\\\ 1 \\\\ 0 \\end{bmatrix}$$?</text>",
                "options": [
                    {
                        "id": "df156ec82816fed9a92e71d24a69a8de",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}4 \\\\ 0 \\\\ 5\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "6687c05563bb97bd9e354e12f927894a",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}-4 \\\\ -1 \\\\ 3\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "57717c11d36c6b832a16012d3b7e9447",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}-4 \\\\ 0 \\\\ 3.5\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "3c41ac9fb365771c86a5b47298ee5fe0",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}0 \\\\ 2 \\\\ 3.5 \\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "57717c11d36c6b832a16012d3b7e9447"
                ],
                "explanation": "",
                "videoCuePoint": 400900
            },
            {
                "id": "cda9dad8fb55efcabea787717102f417",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">What is $$2 \\times \\begin{bmatrix}4 &amp; 5 \\\\ 1 &amp; 7\\end{bmatrix}$$?</text>",
                "options": [
                    {
                        "id": "0fc82c4aee8ac9c5d646dfdd43d618cf",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 8 &amp; 10 \\\\ 2 &amp; 14 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "f1aa006423c170d17073d40753dff0ae",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 8 &amp; 5 \\\\ 1 &amp; 7 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "bbd88f7206eda14b08c3056c84e94dc8",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}8 &amp; 10 \\\\ 1 &amp; 7\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "adec7597e612a36995f3e736fba9db00",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}4 &amp; 5 \\\\ 1 &amp; 14\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "0fc82c4aee8ac9c5d646dfdd43d618cf"
                ],
                "explanation": "",
                "videoCuePoint": 241500
            },
            {
                "id": "cf2a66ef4fcbb82846f7d784de4763eb",
                "type": "mcq",
                "definition": "<text>What is</text><text hasMath=\"true\">$$\\begin{bmatrix} 8 &amp; 6 &amp; 9\\\\ 10 &amp; 1 &amp; 10\\end{bmatrix} + \\begin{bmatrix} 3 &amp; 10 &amp; 2 \\\\ 6 &amp; 1 &amp; -1\\end{bmatrix}$$?</text>",
                "options": [
                    {
                        "id": "0cbb9675af3c85205d180265d88f029f",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 5 &amp; -4  &amp; 7 \\\\ 4 &amp; 0 &amp; 11 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "884a7c7a9f88670878b9989fe5e36e55",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 11 &amp; 16 &amp; 11 \\\\ 16 &amp; 2 &amp; 9 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "328c87463f4491245526aa90a1e07ae0",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix} 14 &amp; 7 &amp; 8 \\\\ 13 &amp; 11 &amp; 12\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "f9089c268b3257d4bfa9fc3981f5ed27",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}8 &amp; 6 &amp; 9 \\\\ 10 &amp; 1 &amp; 10 \\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "884a7c7a9f88670878b9989fe5e36e55"
                ],
                "explanation": "",
                "videoCuePoint": 111500
            }
        ]
    },
    {
        "videoId": "IrleyL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "00eb0e871e6ce85883cddb9d12d566c0",
                "type": "mcq",
                "definition": "<text>Consider the product of these two matrices:</text><text hasMath=\"true\">$$\\begin{bmatrix} 1 &amp; 2 &amp; 1 &amp; 5 \\\\ 0 &amp; 3 &amp; 0 &amp; 4 \\\\ -1 &amp; -2 &amp; 0 &amp; 0 \\end{bmatrix} \\begin{bmatrix} 1 \\\\ 3 \\\\ 2 \\\\ 1 \\end{bmatrix}$$</text><text>What is the dimension of the product?</text>",
                "options": [
                    {
                        "id": "3344257d7957ece1970b99a7ff3bc5e8",
                        "content": "<text hasMath=\"true\">$$3\\times1$$</text>"
                    },
                    {
                        "id": "2313bb2c01172ab252485adedde45334",
                        "content": "<text hasMath=\"true\">$$3\\times4$$</text>"
                    },
                    {
                        "id": "fe034993e6ec3b1d51363c4a2c1fd8c0",
                        "content": "<text hasMath=\"true\">$$1\\times3$$</text>"
                    },
                    {
                        "id": "6328a2a4d859724428d88afdf5408fb1",
                        "content": "<text hasMath=\"true\">$$4\\times4$$</text>"
                    }
                ],
                "answer": [
                    "3344257d7957ece1970b99a7ff3bc5e8"
                ],
                "explanation": "",
                "videoCuePoint": 315000
            },
            {
                "id": "8b4486925af827a18afd8fcaaabbf164",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">What is $$\\begin{bmatrix} 1 &amp; 0 &amp; 3 \\\\ 2 &amp; 1 &amp; 5 \\\\ 3 &amp; 1 &amp; 2 \\end{bmatrix} \\times \\begin{bmatrix} 1 \\\\ 6 \\\\ 2\\end{bmatrix}$$?</text>",
                "options": [
                    {
                        "id": "03e3e1c56f4509305878374654c0f93a",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}5 \\\\ 10 \\\\ 1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "c8fe68ede2e1e0042b17c6352cb87868",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}7 \\\\ 12 \\\\ 7\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "22d890fdf0e5b396c9a3d825cec2f807",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}7 \\\\ 18 \\\\ 13\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "b0e48d14cb27d42a8df2d210e486be63",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}1 \\\\ 18 \\\\ 13\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "22d890fdf0e5b396c9a3d825cec2f807"
                ],
                "explanation": "",
                "videoCuePoint": 448500
            }
        ]
    },
    {
        "videoId": "Irrlab1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e5838670d9efc65d7133f262cd352ab8",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In the equation $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 &amp; 0 \\\\ 2 &amp; 3\\end{bmatrix} = \\begin{bmatrix}7 &amp; 9 \\\\ a &amp; b \\\\ c &amp; d \\end{bmatrix}$$, what is $$b$$?</text><text hasMath=\"true\">Hint: Compute $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 \\\\ 2 \\end{bmatrix}$$ and</text><text hasMath=\"true\">$$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}0 \\\\3\\end{bmatrix}$$.</text>",
                "options": [
                    {
                        "id": "837464b7c72db7743f9c3628d193990b",
                        "content": "<text>7</text>"
                    },
                    {
                        "id": "26defa14d3f52497c3018b23e4441e0f",
                        "content": "<text>10</text>"
                    },
                    {
                        "id": "934c5ef1991422b7d821280e80a8d3c1",
                        "content": "<text>12</text>"
                    },
                    {
                        "id": "e1bb890898566fe47d8786b6821fe549",
                        "content": "<text>15</text>"
                    }
                ],
                "answer": [
                    "934c5ef1991422b7d821280e80a8d3c1"
                ],
                "explanation": "",
                "videoCuePoint": 453500
            },
            {
                "id": "8a904036386999c4f1f6846b687276c3",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In the equation $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 &amp; 0 \\\\ 2 &amp; 3\\end{bmatrix} = \\begin{bmatrix}7 &amp; 9 \\\\ a &amp; b \\\\ c &amp; d \\end{bmatrix}$$, what is $$a$$?</text><text hasMath=\"true\">Hint: Compute $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 \\\\ 2 \\end{bmatrix}$$ and</text><text hasMath=\"true\">$$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}0 \\\\3\\end{bmatrix}$$.</text>",
                "options": [
                    {
                        "id": "cd2007781debc3c9f9fe4fba8c666240",
                        "content": "<text>7</text>"
                    },
                    {
                        "id": "425687ee92a60538c911a9fe2cb5d380",
                        "content": "<text>12</text>"
                    },
                    {
                        "id": "309c78075bbfa143383bbd762b3d52e8",
                        "content": "<text>10</text>"
                    },
                    {
                        "id": "a217d4ad7d521fc199dbb193644799bb",
                        "content": "<text>6</text>"
                    }
                ],
                "answer": [
                    "309c78075bbfa143383bbd762b3d52e8"
                ],
                "explanation": "",
                "videoCuePoint": 453500
            },
            {
                "id": "c8be7aa3a9ad4ddaa7a89759b749d4e5",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In the equation $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 &amp; 0 \\\\ 2 &amp; 3\\end{bmatrix} = \\begin{bmatrix}7 &amp; 9 \\\\ a &amp; b \\\\ c &amp; d \\end{bmatrix}$$, what is $$c$$?</text><text hasMath=\"true\">Hint: Compute $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 \\\\ 2 \\end{bmatrix}$$ and</text><text hasMath=\"true\">$$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}0 \\\\3\\end{bmatrix}$$.</text>",
                "options": [
                    {
                        "id": "1904700183a40a78a8405547665f7d25",
                        "content": "<text>7</text>"
                    },
                    {
                        "id": "ea05a6762c5f52f159970fe160de5a54",
                        "content": "<text>12</text>"
                    },
                    {
                        "id": "8a31eaffa99b0d1048427515147d0ea5",
                        "content": "<text>10</text>"
                    },
                    {
                        "id": "261bddefc353440f841898d16d4a7cec",
                        "content": "<text>15</text>"
                    }
                ],
                "answer": [
                    "8a31eaffa99b0d1048427515147d0ea5"
                ],
                "explanation": "",
                "videoCuePoint": 453500
            },
            {
                "id": "5b2ba42c35aaac2b01cd8a53ea9527d6",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In the equation $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 &amp; 0 \\\\ 2 &amp; 3\\end{bmatrix} = \\begin{bmatrix}7 &amp; 9 \\\\ a &amp; b \\\\ c &amp; d \\end{bmatrix}$$, what is $$d$$?</text><text hasMath=\"true\">Hint: Compute $$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}1 \\\\ 2 \\end{bmatrix}$$ and</text><text hasMath=\"true\">$$\\begin{bmatrix} 1 &amp; 3 \\\\ 2 &amp; 4 \\\\ 0 &amp; 5 \\end{bmatrix}\\begin{bmatrix}0 \\\\3\\end{bmatrix}$$.</text>",
                "options": [
                    {
                        "id": "6624ee078af34a696c5e1b75b1c6ed3b",
                        "content": "<text>8</text>"
                    },
                    {
                        "id": "0606e6c7d80a66d779e7726404593097",
                        "content": "<text>10</text>"
                    },
                    {
                        "id": "7d766e9bab8b9929ab8a95a8d426ea31",
                        "content": "<text>12</text>"
                    },
                    {
                        "id": "33ef71704b26c227767a1ce8bda0e46b",
                        "content": "<text>15</text>"
                    }
                ],
                "answer": [
                    "33ef71704b26c227767a1ce8bda0e46b"
                ],
                "explanation": "",
                "videoCuePoint": 453500
            }
        ]
    },
    {
        "videoId": "Irtamr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "805a2e0fcda986965492bc212f552b86",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">What is $$\\begin{bmatrix} 1 &amp; 0 &amp; 0 \\\\ 0 &amp; 1 &amp; 0 \\\\ 0 &amp; 0 &amp; 1 \\end{bmatrix}\\times\\begin{bmatrix} 1 \\\\ 3 \\\\ 2 \\end{bmatrix}$$?</text>",
                "options": [
                    {
                        "id": "ca5993af294fc39ba6a8ac399fec508e",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}2\\\\3\\\\1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "6d7251327a44f6abcbebcd382842f987",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}2\\\\1\\\\3\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "9dd92b534b3916b1150b36d66a6abd1f",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}1\\\\3\\\\2\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "ec27a7d997b80dfc8d5034f6de005e26",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}1&amp;&amp;3&amp;&amp;2\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "9dd92b534b3916b1150b36d66a6abd1f"
                ],
                "explanation": "",
                "videoCuePoint": 519299
            }
        ]
    },
    {
        "videoId": "Irwd671-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "6f6afdadddd0e0c65c8c99853bfd0663",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">What is $$\\begin{bmatrix}0 &amp; 3 \\\\ 1 &amp; 4 \\end{bmatrix}^T$$?</text>",
                "options": [
                    {
                        "id": "bbf92f895f4d3446977389934a88eb3f",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}0 &amp; 4 \\\\ 1 &amp; 3 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "d8b4298857f0043081302476fe5dd67d",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}4 &amp; 3 \\\\ 1 &amp; 0 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "db022531ce1c28a4c17c36b9a6bc13ad",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}4 &amp; 1 \\\\ 3 &amp; 0 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "46a88833c8fd16152926ce7b8ed50d33",
                        "content": "<text hasMath=\"true\">$$\\begin{bmatrix}0 &amp; 1 \\\\ 3 &amp; 4 \\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "46a88833c8fd16152926ce7b8ed50d33"
                ],
                "explanation": "",
                "videoCuePoint": 578000
            }
        ]
    },
    {
        "videoId": "IryTHL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "791cf62ccc3d917d55572d730369f5d8",
                "type": "mcq",
                "definition": "<table rows=\"6\" columns=\"5\"><tr><td><text hasMath=\"true\">Size (feet)$$^2$$</text></td><td><text>Number of bedrooms</text></td><td><text>Number of floors</text></td><td><text>Age of home (years)</text></td><td><text>Price ($1000)</text></td></tr><tr><td><text>2104</text></td><td><text>5</text></td><td><text>1</text></td><td><text>45</text></td><td><text>460</text></td></tr><tr><td><text>1416</text></td><td><text>3</text></td><td><text>2</text></td><td><text>40</text></td><td><text>232</text></td></tr><tr><td><text>1534</text></td><td><text>3</text></td><td><text>2</text></td><td><text>30</text></td><td><text>315</text></td></tr><tr><td><text>852</text></td><td><text>2</text></td><td><text>1</text></td><td><text>36</text></td><td><text>178</text></td></tr><tr><td><text>...</text></td><td><text>...</text></td><td><text>...</text></td><td><text>...</text></td><td><text>...</text></td></tr></table><text hasMath=\"true\">In the training set above, what is $$x_1^{(4)}$$?</text>",
                "options": [
                    {
                        "id": "01b94121b090ca3c8135ce4ae1ae0814",
                        "content": "<text hasMath=\"true\">The size (in feet$$^2$$) of the 1<sup>st</sup> home in the training set</text>"
                    },
                    {
                        "id": "b432360d7abc1f564e52fd670c3b1ab4",
                        "content": "<text>The age (in years) of the 1<sup>st</sup> home in the training set</text>"
                    },
                    {
                        "id": "89dc6767d288438ac6f0178ff5b0e40c",
                        "content": "<text hasMath=\"true\">The size (in feet$$^2$$) of the 4<sup>th</sup> home in the training set</text>"
                    },
                    {
                        "id": "821268b0413f509c4a155b58a9e0e763",
                        "content": "<text>The age (in years) of the 4<sup>th</sup> home in the training set</text>"
                    }
                ],
                "answer": [
                    "89dc6767d288438ac6f0178ff5b0e40c"
                ],
                "explanation": "",
                "videoCuePoint": 204000
            }
        ]
    },
    {
        "videoId": "Ir0ITb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e54e8c69a65bcbc318b917e38953c209",
                "type": "checkbox",
                "definition": "<text>When there are n features, we define the cost function as</text><text hasMath=\"true\">$$ \\displaystyle J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)})^2$$.</text><text hasMath=\"true\">For linear regression, which of the following are also equivalent and correct definitions of $$J(\\theta)$$?</text>",
                "options": [
                    {
                        "id": "deac2bdac89df36b0158a36172025dc6",
                        "content": "<text hasMath=\"true\">$$J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^{m}(\\theta^T x^{(i)} - y^{(i)})^2$$</text>"
                    },
                    {
                        "id": "16bc75af29f4569c0f32bf01767fe2a8",
                        "content": "<text hasMath=\"true\">$$J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^{m}\\left(\\left(\\sum_{j=0}^{n}\\theta_j x^{(i)}_j\\right) - y^{(i)}\\right)^2$$ (Inner sum starts at 0)</text>"
                    },
                    {
                        "id": "b9bfda99f46ec9c8896e2784b7942065",
                        "content": "<text hasMath=\"true\">$$J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^{m}\\left(\\left(\\sum_{j=1}^{n}\\theta_j x^{(i)}_j\\right) - y^{(i)}\\right)^2$$ (Inner sum starts at 1)</text>"
                    },
                    {
                        "id": "33b0ecb39caed4b1de965122b10df740",
                        "content": "<text hasMath=\"true\">$$J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^{m}\\left(\\left(\\sum_{j=0}^{n}\\theta_j x^{(i)}_j\\right) - \\left(\\sum_{j=0}^{n}y^{(i)}_j\\right)\\right)^2$$</text>"
                    }
                ],
                "answer": [
                    "deac2bdac89df36b0158a36172025dc6",
                    "16bc75af29f4569c0f32bf01767fe2a8"
                ],
                "explanation": "",
                "videoCuePoint": 81500
            }
        ]
    },
    {
        "videoId": "Ir6O7r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "58b4401ec2b72d36407ff4abf7865fce",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you are using a learning algorithm to estimate the price of houses in a city. You want one of your features $$x_i$$ to capture the age of the house. In your training set, all of your houses have an age between 30 and 50 years, with an average age of 38 years. Which of the following would you use as features, assuming you use feature scaling and mean normalization?</text>",
                "options": [
                    {
                        "id": "91732aa35cff5b851a292699a88244bf",
                        "content": "<text hasMath=\"true\">$$\\displaystyle x_i = \\text{age of house}$$</text>"
                    },
                    {
                        "id": "49f65038fee111ea097e99c7b0d1d6c6",
                        "content": "<text hasMath=\"true\">$$\\displaystyle x_i = \\frac{\\text{age of house}}{50}$$</text>"
                    },
                    {
                        "id": "b27c113d330fcf182e866c2b4a4584d0",
                        "content": "<text hasMath=\"true\">$$\\displaystyle x_i = \\frac{\\text{age of house}-38}{50}$$</text>"
                    },
                    {
                        "id": "efcc8ea20b8eff1b74d88a72011872b6",
                        "content": "<text hasMath=\"true\">$$\\displaystyle x_i = \\frac{\\text{age of house}-38}{20}$$</text>"
                    }
                ],
                "answer": [
                    "efcc8ea20b8eff1b74d88a72011872b6"
                ],
                "explanation": "",
                "videoCuePoint": 514500
            }
        ]
    },
    {
        "videoId": "Ir8rL71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "48c58d91e8b4ba69e855527382fd0024",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose a friend ran gradient descent three times, with $$\\alpha = 0.01$$, $$\\alpha = 0.1$$, and $$\\alpha = 1$$, and got the following three plots (labeled A, B, and C):</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/4.4-quiz-1-plots.png\" alt=\"Plot A shows $$J(\\theta)$$ sharply decreasing after the first few iterations, and then leveling off. Plot B shows $$J(\\theta)$$ slowly decreasing at every iteration, and still decreasing at the last iteration. Plot C shows $$J(\\theta)$$ increasing every iteration, with the increase growing in every iteration.\" /><text hasMath=\"true\">Which plots corresponds to which values of $$\\alpha$$?</text>",
                "options": [
                    {
                        "id": "439b299d0d3b8420430a897f2575e809",
                        "content": "<text hasMath=\"true\">A is $$\\alpha=0.01$$, B is $$\\alpha = 0.1$$, C is $$\\alpha =1$$.</text>"
                    },
                    {
                        "id": "dccf33328b0e92882b98ad16cd4a7680",
                        "content": "<text hasMath=\"true\">A is $$\\alpha=0.1$$, B is $$\\alpha = 0.01$$, C is $$\\alpha =1$$.</text>"
                    },
                    {
                        "id": "06a63d651a7c9b4f2da4da9b4961fcb9",
                        "content": "<text hasMath=\"true\">A is $$\\alpha=1$$, B is $$\\alpha = 0.01$$, C is $$\\alpha =0.1$$.</text>"
                    },
                    {
                        "id": "3227ee08ed2cb93cac9873dcc97e3399",
                        "content": "<text hasMath=\"true\">A is $$\\alpha=1$$, B is $$\\alpha = 0.1$$, C is $$\\alpha =0.01$$.</text>"
                    }
                ],
                "answer": [
                    "dccf33328b0e92882b98ad16cd4a7680"
                ],
                "explanation": "<text>In graph C, the cost function is increasing, so the learning rate is set too high. Both graphs A and B converge to an optimum of the cost function, but graph B does so very slowly, so its learning rate is set too low. Graph A lies between the two.</text>",
                "videoCuePoint": 411800
            }
        ]
    },
    {
        "videoId": "Ir95UL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e6c165be4366066b2b12c03a7a73261c",
                "type": "mcq",
                "definition": "<text>Suppose you want to predict a house's price as a function of its size. Your model is </text><text hasMath=\"true\">$$h_\\theta(x) = \\theta_0 + \\theta_1(\\text{size}) + \\theta_2\\sqrt{(\\text{size})}$$. </text><text hasMath=\"true\">Suppose size ranges from 1 to 1000 (feet$$^2$$). You will implement this by fitting a model</text><text hasMath=\"true\">$$h_\\theta(x) = \\theta_0 + \\theta_1x_1 + \\theta_2x_2$$. </text><text>Finally, suppose you want to use feature scaling (without mean normalization).</text><text hasMath=\"true\">Which of the following choices for $$x_1$$ and $$x_2$$ should you use? (Note: $$\\sqrt{1000} \\approx 32$$.)</text>",
                "options": [
                    {
                        "id": "2bd1895e54ce19e404af4bdc16e26776",
                        "content": "<text hasMath=\"true\">$$x_1 = \\text{size},\\ x_2 = 32\\sqrt{(\\text{size})}$$</text>"
                    },
                    {
                        "id": "be2141036e13daf0deeb0038ea5e741e",
                        "content": "<text hasMath=\"true\">$$x_1=32(\\text{size}),\\ x_2=\\sqrt{(\\text{size})}$$</text>"
                    },
                    {
                        "id": "b1b92acc82e8f1255bdb2b7e96baf44b",
                        "content": "<text hasMath=\"true\">$$x_1 = \\frac{\\text{size}}{1000},\\ x_2 = \\frac{\\sqrt{(\\text{size})}}{32}$$</text>"
                    },
                    {
                        "id": "81ae16d803376b3bbb50d3df1185dfaa",
                        "content": "<text hasMath=\"true\">$$x_1 = \\frac{\\text{size}}{32},\\ x_2=\\sqrt{(\\text{size})}$$.</text>"
                    }
                ],
                "answer": [
                    "b1b92acc82e8f1255bdb2b7e96baf44b"
                ],
                "explanation": "",
                "videoCuePoint": 395100
            }
        ]
    },
    {
        "videoId": "IsEnAb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e6c165be4366066b2b12c03a7a73261c",
                "type": "mcq",
                "definition": "<text>Suppose you have the training in the table below:</text><table rows=\"4\" columns=\"3\"><tr><td><text hasMath=\"true\">age ($$x_1$$)</text></td><td><text hasMath=\"true\">height in cm ($$x_2$$)</text></td><td><text hasMath=\"true\">weight in kg ($$y$$)</text></td></tr><tr><td><text>4</text></td><td><text>89</text></td><td><text>16</text></td></tr><tr><td><text>9</text></td><td><text>124</text></td><td><text>28</text></td></tr><tr><td><text>5</text></td><td><text>103</text></td><td><text>20</text></td></tr></table><text>You would like to predict a child's weight as a function of his age and height with the model </text><text hasMath=\"true\">$$\\text{weight} = \\theta_0 + \\theta_1\\text{age}+\\theta_2\\text{height}$$.</text><text hasMath=\"true\">What are $$X$$ and $$y$$?</text>",
                "options": [
                    {
                        "id": "2bd1895e54ce19e404af4bdc16e26776",
                        "content": "<text hasMath=\"true\">$$X=\\begin{bmatrix} 4 &amp; 89 \\\\ 9 &amp; 124 \\\\ 5 &amp; 103 \\end{bmatrix},\\ y=\\begin{bmatrix}16\\\\28\\\\20\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "be2141036e13daf0deeb0038ea5e741e",
                        "content": "<text hasMath=\"true\">$$X=\\begin{bmatrix} 1 &amp; 4 &amp; 89 \\\\ 1 &amp;9 &amp; 124 \\\\ 1 &amp; 5 &amp; 103 \\end{bmatrix},\\ y=\\begin{bmatrix}1 &amp; 16 \\\\ 1 &amp; 28 \\\\ 1 &amp; 20 \\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "b1b92acc82e8f1255bdb2b7e96baf44b",
                        "content": "<text hasMath=\"true\">$$X=\\begin{bmatrix} 4 &amp; 89 &amp; 1 \\\\ 9 &amp; 124 &amp; 1 \\\\ 5 &amp; 103 &amp; 1 \\end{bmatrix},\\ y=\\begin{bmatrix}16\\\\28\\\\20\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "81ae16d803376b3bbb50d3df1185dfaa",
                        "content": "<text hasMath=\"true\">$$X=\\begin{bmatrix} 1 &amp; 4 &amp; 89 \\\\ 1 &amp; 9 &amp; 124 \\\\ 1 &amp; 5 &amp; 103 \\end{bmatrix},\\ y=\\begin{bmatrix}16\\\\28\\\\20\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "81ae16d803376b3bbb50d3df1185dfaa"
                ],
                "explanation": "",
                "videoCuePoint": 524600
            }
        ]
    },
    {
        "videoId": "IsHDQr1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "Isfdyb1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IsI4c71-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IsTQhL1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IsVFtb1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IsWT1r1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IsePqL1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "IsdBh71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "2f34f3972ff9229b54de55e22962e138",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you have three vector valued variables $$u, v, w$$:</text><text hasMath=\"true\">$$u = \\begin{bmatrix}u_1\\\\u_2\\\\u_3\\end{bmatrix},\\ v = \\begin{bmatrix}v_1\\\\v_2\\\\v_3\\end{bmatrix},\\ w = \\begin{bmatrix}w_1\\\\w_2\\\\w_3\\end{bmatrix}$$.</text><text>Your code implements the following:</text><text>for j = 1:3,</text><text>    u(j) = 2 * v(j) + 5 * w(j);</text><text>end</text><text>How would you vectorize this code?</text>",
                "options": [
                    {
                        "id": "2988c087bd68e0b4ca5d6bd4d8af3f07",
                        "content": "<text>u = 2 * v' * v * w + 5 * w' * w * v; (where v' denotes the transpose of v)</text>"
                    },
                    {
                        "id": "c43e57ce66c7e4611bebdd6ad6b76c08",
                        "content": "<text>u = 2 * v + 5 * w</text>"
                    },
                    {
                        "id": "b1c3e83da4d479d56944caeea9508ec2",
                        "content": "<text>u = 5 * v + 2 * w</text>"
                    },
                    {
                        "id": "703cfb71ae7bdea8396b9440c3c1fa18",
                        "content": "<text>u = 2 + v + 5 + w</text>"
                    }
                ],
                "answer": [
                    "c43e57ce66c7e4611bebdd6ad6b76c08"
                ],
                "explanation": "",
                "videoCuePoint": 787800
            }
        ]
    },
    {
        "videoId": "Isgr6r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "70b8c6c56af273d8bfa4e170fcaf94e9",
                "type": "mcq",
                "definition": "<text>Which of the following statements is true?</text>",
                "options": [
                    {
                        "id": "e88acd99c3d9dadf452a70e100c8ffbe",
                        "content": "<text>If linear regression doesn't work on a classification task as in the previous example shown in the video, applying feature scaling may help.</text>"
                    },
                    {
                        "id": "3b81892cd29fcccfdf48f51f15acd95b",
                        "content": "<text hasMath=\"true\">If the training set satisfies $$0 \\leq y^{(i)} \\leq 1$$ for every training example $$(x^{(i)},y^{(i)})$$, then linear regression's prediction will also satisfy $$0 \\leq h_\\theta(x) \\leq 1$$ for all values of $$x$$.</text>"
                    },
                    {
                        "id": "aa7fc313d0a3ebfa964b20833f25b5a5",
                        "content": "<text hasMath=\"true\">If there is a feature $$x$$ that perfectly predicts $$y$$, i.e. if $$y=1$$ when $$x\\geq c$$ and $$y=0$$ whenever $$x &lt; c$$ (for some constant $$c$$), then linear regression will obtain zero classification error.</text>"
                    },
                    {
                        "id": "b830e967f7bf7ce1b0788c2e1800896a",
                        "content": "<text>None of the above statements are true.</text>"
                    }
                ],
                "answer": [
                    "b830e967f7bf7ce1b0788c2e1800896a"
                ],
                "explanation": "",
                "videoCuePoint": 427500
            }
        ]
    },
    {
        "videoId": "Ismyi71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "1d036ffe94adadf12d016373ece24900",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose we want to predict, from data $$x$$ about a tumor, whether it is malignant ($$y=1$$) or benign ($$y=0$$). Our logistic regression classifier outputs, for a specific tumor, $$h_\\theta(x) = P(y=1\\vert x;\\theta) = 0.7$$, so we estimate that there is a 70% chance of this tumor being malignant. What should be our estimate for $$P(y=0\\vert x;\\theta)$$, the probability the tumor is benign? </text>",
                "options": [
                    {
                        "id": "8fbdf0f130e2c27fe59cff00c5c832da",
                        "content": "<text hasMath=\"true\">$$P(y=0\\vert x;\\theta) = 0.3$$</text>"
                    },
                    {
                        "id": "0c090beb1d6a059736cbc7a299b9f783",
                        "content": "<text hasMath=\"true\">$$P(y=0\\vert x;\\theta) = 0.7$$</text>"
                    },
                    {
                        "id": "689c390bf9f4f7941f8d005199330e83",
                        "content": "<text hasMath=\"true\">$$P(y=0\\vert x;\\theta) = 0.7^2$$</text>"
                    },
                    {
                        "id": "e20becd1df2d94f7d0cb6a2d86f11530",
                        "content": "<text hasMath=\"true\">$$P(y=0\\vert x;\\theta) = 0.3\\times 0.7$$</text>"
                    }
                ],
                "answer": [
                    "8fbdf0f130e2c27fe59cff00c5c832da"
                ],
                "explanation": "",
                "videoCuePoint": 338900
            }
        ]
    },
    {
        "videoId": "IsonvL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e5673e3958bf0966215b10e527f5644b",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider logistic regression with two features $$x_1$$ and $$x_2$$. Suppose $$\\theta_0 = 5$$, $$\\theta_1 = -1$$, $$\\theta_2 = 0$$, so that $$h_\\theta(x) = g(5 - x_1)$$. Which of these shows the decision boundary of $$h_\\theta(x)$$?</text>",
                "options": [
                    {
                        "id": "1c0883c0ec4fb83305b1390ef3c6da87",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.3-quiz-1-option1.png\" alt=\"\" /><text> .</text>"
                    },
                    {
                        "id": "6c745e22607406b05a6b6f4086199e0c",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.3-quiz-1-option2.png\" alt=\"\" /><text> .</text>"
                    },
                    {
                        "id": "340b82c30f762632e6c757de8d5c90c6",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.3-quiz-1-option3.png\" alt=\"\" /><text> .</text>"
                    },
                    {
                        "id": "89e32bf07f43bcac07e0e91e6cb15d69",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.3-quiz-1-option4.png\" alt=\"\" /><text> .</text>"
                    }
                ],
                "answer": [
                    "1c0883c0ec4fb83305b1390ef3c6da87"
                ],
                "explanation": "<text hasMath=\"true\">Predict Y = 0 if $$x_1$$ is greater than 5.</text>",
                "videoCuePoint": 587700
            }
        ]
    },
    {
        "videoId": "-fkmg-RqEeag_AqHbNH9MA",
        "questions": [
            {
                "id": "b525479091f6e8ab9e080e8b1fd747cb",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider minimizing a cost function $$J(\\theta)$$. Which one of these functions is convex?</text>",
                "options": [
                    {
                        "id": "5985204430d0d15caf4c34a9e4df1aae",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.4-quiz-1-option1.png\" alt=\"\" /><text>.</text>"
                    },
                    {
                        "id": "fd61f54aee4ed62b332c33a252f71356",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.4-quiz-1-option2.png\" alt=\"\" /><text>.</text>"
                    },
                    {
                        "id": "6b4b0e0aa9131865b5f47b7534046561",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.4-quiz-1-option3.png\" alt=\"\" /><text>.</text>"
                    },
                    {
                        "id": "2a20d24aa77eaff61320d9f3a1ebcc2e",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/6.4-quiz-1-option4.png\" alt=\"\" /><text>.</text>"
                    }
                ],
                "answer": [
                    "fd61f54aee4ed62b332c33a252f71356"
                ],
                "explanation": "",
                "videoCuePoint": 270000
            },
            {
                "id": "cb22bb7a05d07a6948215d0e7f160b48",
                "type": "checkbox",
                "definition": "<text hasMath=\"true\">In logistic regression, the cost function for our hypothesis outputting (predicting) $$h_\\theta(x)$$ on a training example that has label $$y\\in\\{0,1\\}$$ is:</text><text hasMath=\"true\">$$\\text{cost}(h_\\theta(x),y) = \\left\\{ \\begin{array}{ll}    -\\log h_\\theta(x) &amp; \\text{if }y=1\\\\   -\\log(1-h_\\theta(x)) &amp; \\text{if }y=0 \\end{array}\\right.$$</text><text>Which of the following are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "b66f050294a2bc730aa2a4bc06d5fe65",
                        "content": "<text hasMath=\"true\">If $$h_\\theta(x) = y$$, then $$\\text{cost}(h_\\theta(x),y) = 0$$ (for $$y=0$$ and $$y=1$$).</text>"
                    },
                    {
                        "id": "228f6d045455fad221461cab3802bf4e",
                        "content": "<text hasMath=\"true\">If $$y=0$$, then $$\\text{cost}(h_\\theta(x),y)\\rightarrow\\infty$$ as $$h_\\theta(x)\\rightarrow 1$$.</text>"
                    },
                    {
                        "id": "753f5245162b81958505fd721bca70a2",
                        "content": "<text hasMath=\"true\">If $$y=0$$, then $$\\text{cost}(h_\\theta(x),y)\\rightarrow\\infty$$ as $$h_\\theta(x)\\rightarrow 0$$.</text>"
                    },
                    {
                        "id": "9932b9b9ddf18a8e93a2c0a704719c60",
                        "content": "<text hasMath=\"true\">Regardless of whether $$y=0$$ or $$y=1$$, if $$h_\\theta(x)=0.5$$, then $$\\text{cost}(h_\\theta(x),y) &gt; 0$$.</text>"
                    }
                ],
                "answer": [
                    "b66f050294a2bc730aa2a4bc06d5fe65",
                    "228f6d045455fad221461cab3802bf4e",
                    "9932b9b9ddf18a8e93a2c0a704719c60"
                ],
                "explanation": "",
                "videoCuePoint": 577500
            }
        ]
    },
    {
        "videoId": "Isp13b1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5fb0393c15b1e33b2697739238828372",
                "type": "mcq",
                "definition": "<text>One iteration of gradient descent simultaneously performs these updates:</text><text hasMath=\"true\">$$\\theta_0 := \\theta_0 - \\alpha\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)}) \\cdot x^{(i)}_0$$</text><text hasMath=\"true\">$$\\theta_1 := \\theta_1 - \\alpha\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)}) \\cdot x^{(i)}_1$$</text><text hasMath=\"true\">$$\\vdots$$</text><text hasMath=\"true\">$$\\theta_n := \\theta_n - \\alpha\\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)}) \\cdot x^{(i)}_n$$</text><text hasMath=\"true\">We would like a vectorized implementation of the form $$\\theta := \\theta - \\alpha\\delta$$ (for some vector $$\\delta\\in\\mathbb{R}^{n+1}$$).</text><text>What should the vectorized implementation be?</text>",
                "options": [
                    {
                        "id": "c5bbfa4a9218462e66a3a11ee3ee72f5",
                        "content": "<text hasMath=\"true\">$$\\theta := \\theta - \\alpha\\frac{1}{m}\\sum_{i=1}^{m}[(h_\\theta(x^{(i)}) - y^{(i)}) \\cdot x^{(i)}]$$</text>"
                    },
                    {
                        "id": "d225b65632d93143b347f29f00de432f",
                        "content": "<text hasMath=\"true\">$$\\theta := \\theta - \\alpha\\frac{1}{m}[\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)})] \\cdot x^{(i)}$$</text>"
                    },
                    {
                        "id": "8456497bc7ec5ae40729c2a7aa32248d",
                        "content": "<text hasMath=\"true\">$$\\theta := \\theta - \\alpha\\frac{1}{m}x^{(i)}[\\sum_{i=1}^{m}(h_\\theta(x^{(i)}) - y^{(i)})]$$</text>"
                    },
                    {
                        "id": "3da9983f4a41331afe1747f6d3019279",
                        "content": "<text>All of the above are correct implementations.</text>"
                    }
                ],
                "answer": [
                    "c5bbfa4a9218462e66a3a11ee3ee72f5"
                ],
                "explanation": "",
                "videoCuePoint": 569800
            },
            {
                "id": "e20066c3ca636a3a383f6df848851d75",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you are running gradient descent to fit a logistic regression model with parameter $$\\theta\\in\\mathbb{R}^{n+1}$$. Which of the following is a reasonable way to make sure the learning rate $$\\alpha$$ is set properly and that gradient descent is running correctly?</text>",
                "options": [
                    {
                        "id": "5f3873a3d7653ebe1f301fd4c427110b",
                        "content": "<text hasMath=\"true\">Plot $$J(\\theta) = \\frac{1}{m}\\sum_{i=1}^{m}(h_\\theta(x^{(i)})-y^{(i)})^2$$ as a function of the number of iterations (i.e. the horizontal axis is the iteration number) and make sure $$J(\\theta)$$ is decreasing on every iteration.</text>"
                    },
                    {
                        "id": "df03d1b2367037cbd6137c54ab4f9809",
                        "content": "<text hasMath=\"true\">Plot $$J(\\theta) = -\\frac{1}{m}\\sum_{i=1}^{m}[y^{(i)}\\log h_\\theta(x^{(i)}) + (1-y^{(i)})\\log(1-h_\\theta(x^{(i)}))]$$ as a function of the number of iterations and make sure $$J(\\theta)$$ is decreasing on every iteration.</text>"
                    },
                    {
                        "id": "07b8ca172c4509651b6ef72a99c8ea5f",
                        "content": "<text hasMath=\"true\">Plot $$J(\\theta)$$ as a function of $$\\theta$$ and make sure it is decreasing on every iteration.</text>"
                    },
                    {
                        "id": "f181b1aeb9e681df962dbb4a2edd898e",
                        "content": "<text hasMath=\"true\">Plot $$J(\\theta)$$ as a function of $$\\theta$$ and make sure it is convex.</text>"
                    }
                ],
                "answer": [
                    "df03d1b2367037cbd6137c54ab4f9809"
                ],
                "explanation": "",
                "videoCuePoint": 523600
            }
        ]
    },
    {
        "videoId": "IsrrDr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "lZ9H8bLrEeSTXyIACzQGuw@5",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you want to use an advanced optimization algorithm to minimize the cost function for logistic regression with parameters $$\\theta_0$$ and $$\\theta_1$$. You write the following code:</text><img src=\"https://coursera-forum-screenshots.s3.amazonaws.com/14/cead80d82b11e4b390fb94e489e9db/Screen-Shot-2015-03-31-at-9.52.10-PM.png\" /><text>What should CODE#1 and CODE#2 above compute?</text>",
                "options": [
                    {
                        "id": "e9599079e4a528808e54b13142e94c63",
                        "content": "<text hasMath=\"true\">CODE#1 and CODE#2 should compute $$J(\\theta)$$.</text>"
                    },
                    {
                        "id": "05826f4b781a25d1cecae26174f83fd9",
                        "content": "<text>CODE#1 should be theta(1) and CODE#2 should be theta(2).</text>"
                    },
                    {
                        "id": "692cd8128be091f271b217ba4ce6f606",
                        "content": "<text hasMath=\"true\">CODE#1 should compute $$\\frac{1}{m}\\sum_{i=1}^m[(h_\\theta(x^{(i)}) - y^{(i)})\\cdot x^{(i)}_0] (= \\frac{\\partial}{\\partial\\theta_0}J(\\theta))$$, and</text><text hasMath=\"true\">&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;&#xa0;CODE#2 should compute $$\\frac{1}{m}\\sum_{i=1}^m[(h_\\theta(x^{(i)}) - y^{(i)})\\cdot x^{(i)}_1] (= \\frac{\\partial}{\\partial\\theta_1}J(\\theta))$$.</text>"
                    },
                    {
                        "id": "35ab3397a278515bed27bc4597ab7cbf",
                        "content": "<text>None of the above.</text>"
                    }
                ],
                "answer": [
                    "692cd8128be091f271b217ba4ce6f606"
                ],
                "explanation": "",
                "videoCuePoint": 794500
            }
        ]
    },
    {
        "videoId": "Is9X371-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "525304f1c63b25d3c91039c84fb7f7f1",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you have a multi-class classification problem with $$k$$ classes (so $$y\\in \\{1,2,\\dots,k\\}$$). Using the 1-vs.-all method, how many different logistic regression classifiers will you end up training?</text>",
                "options": [
                    {
                        "id": "f4d3660011196aef819c169e5afa615c",
                        "content": "<text hasMath=\"true\">$$k-1$$</text>"
                    },
                    {
                        "id": "8e7f6c81989ee0cd9e7bbc52d2a196f0",
                        "content": "<text hasMath=\"true\">$$k$$</text>"
                    },
                    {
                        "id": "d54c664fb53730f7b32c690cb680479c",
                        "content": "<text hasMath=\"true\">$$k+1$$</text>"
                    },
                    {
                        "id": "9016bd4e36f1b3319558c7d587d070e2",
                        "content": "<text hasMath=\"true\">Approximately $$\\log_2(k)$$</text>"
                    }
                ],
                "answer": [
                    "8e7f6c81989ee0cd9e7bbc52d2a196f0"
                ],
                "explanation": "",
                "videoCuePoint": 361500
            }
        ]
    },
    {
        "videoId": "Is_zIL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "fd3185c5e99048a2176cba5c8e2e47b8",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider the medical diagnosis problem of classifying tumors as malignant or benign. If a hypothesis $$h_\\theta(x)$$ has overfit the training set, it means that:</text>",
                "options": [
                    {
                        "id": "e0773a54c14b23fdfbbf2fff8f5c13b9",
                        "content": "<text>It makes accurate predictions for examples in the training set and generalizes well to make accurate predictions on new, previously unseen examples.</text>"
                    },
                    {
                        "id": "f2f63b446e8e6a5dce02f3fb01bb0aea",
                        "content": "<text>It does not make accurate predictions for examples in the training set, but it does generalize well to make accurate predictions on new, previously unseen examples.</text>"
                    },
                    {
                        "id": "4629ef070bf4a2cf2ba69530d3b528d6",
                        "content": "<text>It makes accurate predictions for examples in the training set, but it does not generalize well to make accurate predictions on new, previously unseen examples.</text>"
                    },
                    {
                        "id": "2cef1cb77325680eefe8238ef94feb80",
                        "content": "<text>It does not make accurate predictions for examples in the training set and does not generalize well to make accurate predictions on new, previously unseen examples.</text>"
                    }
                ],
                "answer": [
                    "4629ef070bf4a2cf2ba69530d3b528d6"
                ],
                "explanation": "",
                "videoCuePoint": 363800
            }
        ]
    },
    {
        "videoId": "ItBoUb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5c05be748857f196ed7b9e53c1b3ce7e",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In regularized linear regression, we choose $$\\theta$$ to minimize:</text><text hasMath=\"true\">$$\\displaystyle J(\\theta) = \\frac{1}{2m}\\left[\\sum_{i=1}^m(h_\\theta(x^{(i)}) - y^{(i)})^2 + \\lambda\\sum_{j=1}^n\\theta_j^2\\right]$$</text><text hasMath=\"true\">What if $$\\lambda$$ is set to an extremely large value (perhaps too large for our problem, say $$\\lambda=10^{10}$$)?</text>",
                "options": [
                    {
                        "id": "d2b530b3532acb9b7d47f9da8307c51d",
                        "content": "<text hasMath=\"true\">Algorithm works fine; setting $$\\lambda$$ to be very large can't hurt it.</text>"
                    },
                    {
                        "id": "8f6160edc33de27db68d44ee41e69b4f",
                        "content": "<text>Algorithm fails to eliminate overfitting.</text>"
                    },
                    {
                        "id": "055e91c36d044031948eee23a592b4ea",
                        "content": "<text>Algorithm results in underfitting (fails to fit even the training set).</text>"
                    },
                    {
                        "id": "c69a8e081cea2aa4b83dba574d7633f8",
                        "content": "<text>Gradient descent will fail to converge.</text>"
                    }
                ],
                "answer": [
                    "055e91c36d044031948eee23a592b4ea"
                ],
                "explanation": "",
                "videoCuePoint": 479700
            }
        ]
    },
    {
        "videoId": "ItIWAr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "da7d98e2c5f96e59b3df6f6f06b23d4d",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you are doing gradient descent on a training set of $$m &gt; 0$$ examples, using a fairly small learning rate $$\\alpha &gt; 0$$ and some regularization parameter $$\\lambda &gt; 0$$. Consider the update rule:</text><text hasMath=\"true\">$$\\displaystyle \\theta_j := \\theta_j(1-\\alpha\\frac{\\lambda}{m}) - \\alpha\\frac{1}{m}\\sum_{i=1}^m(h_\\theta(x^{(i)})-y^{(i)})x^{(i)}_j$$.</text><text hasMath=\"true\">Which of the following statements about the term $$(1-\\alpha\\frac{\\lambda}{m})$$ must be true?</text>",
                "options": [
                    {
                        "id": "e80535bb288233b54f25cd1343cdadd8",
                        "content": "<text hasMath=\"true\">$$1-\\alpha\\frac{\\lambda}{m} &gt; 1$$</text>"
                    },
                    {
                        "id": "f83d18a59277480d53ee91c07d15301c",
                        "content": "<text hasMath=\"true\">$$1-\\alpha\\frac{\\lambda}{m} = 1$$</text>"
                    },
                    {
                        "id": "d14d16434a9fcc75bb5d9a15c7fe8821",
                        "content": "<text hasMath=\"true\">$$1-\\alpha\\frac{\\lambda}{m} &lt; 1$$</text>"
                    },
                    {
                        "id": "d315a19cc33d580df0eee793ccf63423",
                        "content": "<text>None of the above.</text>"
                    }
                ],
                "answer": [
                    "d14d16434a9fcc75bb5d9a15c7fe8821"
                ],
                "explanation": "",
                "videoCuePoint": 222300
            }
        ]
    },
    {
        "videoId": "ItMAY71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "3a56e066f61c9859ce51ff3c58a5c586",
                "type": "mcq",
                "definition": "<text>When using regularized logistic regression, which of these is the best way to monitor whether gradient descent is working correctly?</text>",
                "options": [
                    {
                        "id": "3844faafcefd7bb41b70de23560ac29a",
                        "content": "<text hasMath=\"true\">Plot $$-[\\frac{1}{m}\\sum_{i=1}^m y^{(i)}\\log h_\\theta(x^{(i)}) + (1-y^{(i)})\\log(1-h_\\theta(x^{(i)}))]$$ as a function of the number of iterations and make sure it's decreasing.</text>"
                    },
                    {
                        "id": "83409e9410d5e30a61c9ba79c1db8e44",
                        "content": "<text hasMath=\"true\">Plot $$-[\\frac{1}{m}\\sum_{i=1}^m y^{(i)}\\log h_\\theta(x^{(i)}) + (1-y^{(i)})\\log(1-h_\\theta(x^{(i)}))] - \\frac{\\lambda}{2m}\\sum_{j=1}^n\\theta_j^2$$ as a function of the number of iterations and make sure it's decreasing.</text>"
                    },
                    {
                        "id": "133147b33a560d938c01669362472064",
                        "content": "<text hasMath=\"true\">Plot $$-[\\frac{1}{m}\\sum_{i=1}^m y^{(i)}\\log h_\\theta(x^{(i)}) + (1-y^{(i)})\\log(1-h_\\theta(x^{(i)}))] + \\frac{\\lambda}{2m}\\sum_{j=1}^n\\theta_j^2$$ as a function of the number of iterations and make sure it's decreasing.</text>"
                    },
                    {
                        "id": "ff8f2d0c472cb21336247fa18f104fae",
                        "content": "<text hasMath=\"true\">Plot $$\\sum_{j=1}^n\\theta_j^2$$ as a function of the number of iterations and make sure it's decreasing.</text>"
                    }
                ],
                "answer": [
                    "133147b33a560d938c01669362472064"
                ],
                "explanation": "",
                "videoCuePoint": 234600
            }
        ]
    },
    {
        "videoId": "ItN1lL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5433995b83ec4c858532e4f3f8eb5f9d",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you are learning to recognize cars from $$100\\times100$$ pixel images (grayscale, not RGB). Let the features be pixel intensity values. If you train logistic regression including all the quadratic terms ($$x_ix_j$$) as features, about how many features will you have?</text>",
                "options": [
                    {
                        "id": "0c06676eaf30cea42a691281879e61f4",
                        "content": "<text>5,000</text>"
                    },
                    {
                        "id": "49eda177bfd6067e3e7f2f9a36412a63",
                        "content": "<text>100,000</text>"
                    },
                    {
                        "id": "96fd218be9639d35e79e015f407b7c40",
                        "content": "<text hasMath=\"true\">50 million ($$5\\times10^7$$)</text>"
                    },
                    {
                        "id": "6967d79924556619d023dec03c45cc16",
                        "content": "<text hasMath=\"true\">5 billion ($$5\\times10^9$$)</text>"
                    }
                ],
                "answer": [
                    "96fd218be9639d35e79e015f407b7c40"
                ],
                "explanation": "",
                "videoCuePoint": 534700
            }
        ]
    },
    {
        "videoId": "ItPDtb1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "ItVxZr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "103b548649cabfdc5f8f0d5e16b2ed27",
                "type": "mcq",
                "definition": "<text>Consider the following neural network:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.3-quiz-1-q.png\" alt=\"\" /><text hasMath=\"true\">What is the dimension of $$\\Theta^{(1)}$$ (Hint: add a bias unit to the input and hidden layers)?</text><text /><text />",
                "options": [
                    {
                        "id": "0776a87be863d99ddf36d21982b71625",
                        "content": "<text hasMath=\"true\">$$2\\times4$$</text>"
                    },
                    {
                        "id": "4f5540bda6187595a0ba84805d48efae",
                        "content": "<text hasMath=\"true\">$$4\\times2$$</text>"
                    },
                    {
                        "id": "6700da56ed2781a8b471f71812cdc58a",
                        "content": "<text hasMath=\"true\">$$3\\times4$$</text>"
                    },
                    {
                        "id": "e46df226fcca799c0cef55a2704bc9df",
                        "content": "<text hasMath=\"true\">$$4\\times3$$</text>"
                    }
                ],
                "answer": [
                    "e46df226fcca799c0cef55a2704bc9df"
                ],
                "explanation": "",
                "videoCuePoint": 702300
            }
        ]
    },
    {
        "videoId": "ItXml71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "7a1807638d9a042ef8e072bad4fd3bb1",
                "type": "mcq",
                "definition": "<text>Consider the network:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.4-quiz-1-q.png\" alt=\"A four-layer neural network with full connections. There are 3 inputs, 3 units in the first hidden layer, 2 units in the second hidden layer, and one output unit. The inputs are labeled x_1, x_2, and x_3.\" /><text hasMath=\"true\">Let $$a^{(1)} = x \\in \\mathbb{R}^{n+1}$$ denote the input (with $$a^{(1)}_0 = 1$$). </text><text hasMath=\"true\"> How would you compute $$a^{(2)}$$?</text>",
                "options": [
                    {
                        "id": "c6d3313ac0ae54e5f68a255ddfb56552",
                        "content": "<text hasMath=\"true\">$$a^{(2)} = \\Theta^{(1)}a^{(1)}$$</text>"
                    },
                    {
                        "id": "925185b5e0eff266d6116435d34607f6",
                        "content": "<text hasMath=\"true\">$$z^{(2)} = \\Theta^{(2)}a^{(1)};\\ a^{(2)} = g(z^{(2)})$$</text>"
                    },
                    {
                        "id": "da90fb9d415abd0568acc9d1f8ac022f",
                        "content": "<text hasMath=\"true\">$$z^{(2)} = \\Theta^{(1)}a^{(1)};\\ a^{(2)} = g(z^{(2)})$$</text>"
                    },
                    {
                        "id": "9e13c31bcf0bc2c7ce41fef50ad19ffb",
                        "content": "<text hasMath=\"true\">$$z^{(2)} = \\Theta^{(2)}g(a^{(1)});\\ a^{(2)} = g(z^{(2)})$$</text>"
                    }
                ],
                "answer": [
                    "da90fb9d415abd0568acc9d1f8ac022f"
                ],
                "explanation": "",
                "videoCuePoint": 651000
            }
        ]
    },
    {
        "videoId": "Itap6L1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "6c4a5f15785489d0b24cd7d41f0deb3d",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose $$x_1$$ and $$x_2$$ are binary valued (0 or 1). What boolean function does the network shown below (approximately) compute? (Hint: One possible way to answer this is to draw out a truth table, similar to what we did in the video).</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.5-quiz-1-q.png\" alt=\"A two-layer neural network, with two inputs and one output. Weights from the input layer: 20 from x_1 and x_2, and -10 from the bias unit.\" />",
                "options": [
                    {
                        "id": "32bb9e37cabb2d579e038c3a6a130518",
                        "content": "<text hasMath=\"true\">$$x_1$$ AND $$x_2$$</text>"
                    },
                    {
                        "id": "5a534b31968e72f048c1d0971957c885",
                        "content": "<text hasMath=\"true\">(NOT $$x_1$$) OR (NOT $$x_2$$)</text>"
                    },
                    {
                        "id": "917b91a34f695f98fdc2ebbe3ea450a4",
                        "content": "<text hasMath=\"true\">$$x_1$$ OR $$x_2$$</text>"
                    },
                    {
                        "id": "a25f659695d47505bd11156f1ca1af4e",
                        "content": "<text hasMath=\"true\">(NOT $$x_1$$) AND (NOT $$x_2$$)</text>"
                    }
                ],
                "answer": [
                    "917b91a34f695f98fdc2ebbe3ea450a4"
                ],
                "explanation": "",
                "videoCuePoint": 375600
            }
        ]
    },
    {
        "videoId": "Itb4Cb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "6a3dddb6b2ba7c23fc7726c691894c02",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose that $$x_1$$ and $$x_2$$ are binary valued (0 or 1). Which of the following networks (approximately) computes the boolean function (NOT $$x_1$$) AND (NOT $$x_2$$)?</text>",
                "options": [
                    {
                        "id": "bfe006c56d761d75f1756f8a02b59bd2",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.6-quiz-1-option1.png\" alt=\"A two-layer neural network with two inputs and one output. The weights from the input layer are: -20 from x_1, -20 from x_2, and 10 from the bias unit.\" />"
                    },
                    {
                        "id": "4b43621197457c694be20a91fc2020f4",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.6-quiz-1-option2.png\" alt=\"A two-layer neural network with two inputs and one output. The weights from the input layer are: 20 from x_1, 20 from x_2, and -10 from the bias unit.\" />"
                    },
                    {
                        "id": "d5b8769204879ceab88e278a4eb65176",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.6-quiz-1-option3.png\" alt=\"A two-layer neural network with two inputs and one output. The weights from the input layer are: -20 from x_1, -20 from x_2, and 30 from the bias unit.\" />"
                    },
                    {
                        "id": "0039c195259e7d8184c134c4b216354c",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/8.6-quiz-1-option4.png\" alt=\"A two-layer neural network with two inputs and one output. The weights from the input layer are: 20 from x_1, 30 from x_2, and 20 from the bias unit.\" />"
                    }
                ],
                "answer": [
                    "bfe006c56d761d75f1756f8a02b59bd2"
                ],
                "explanation": "",
                "videoCuePoint": 151600
            }
        ]
    },
    {
        "videoId": "ItdGKr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "f6ae5fa4fcb77394ea1b126f11f16645",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you have a multi-class classification problem with 10 classes. Your neural network has 3 layers, and the hidden layer (layer 2) has 5 units. Using the one-vs-all method described here, how many elements does $$\\Theta^{(2)}$$ have?</text>",
                "options": [
                    {
                        "id": "2162f01cfcca1fbda7103afb23ecdf67",
                        "content": "<text>50</text>"
                    },
                    {
                        "id": "0e678f735fa322a20d82a8e9686e7c3c",
                        "content": "<text>55</text>"
                    },
                    {
                        "id": "ccba49a828c2d8b172f0721163f5ded8",
                        "content": "<text>60</text>"
                    },
                    {
                        "id": "0d90dc8d9ba6014a692013a83c1abc32",
                        "content": "<text>66</text>"
                    }
                ],
                "answer": [
                    "ccba49a828c2d8b172f0721163f5ded8"
                ],
                "explanation": "",
                "videoCuePoint": 211500
            }
        ]
    },
    {
        "videoId": "Ite7W71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "885ec8468d4fe42b64fb743cc13da6c2",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose we want to try to minimize $$J(\\Theta)$$ as a function of $$\\Theta$$, using one of the advanced optimization methods (fminunc, conjugate gradient, BFGS, L-BFGS, etc.). What do we need to supply code to compute (as a function of $$\\Theta$$)?</text>",
                "options": [
                    {
                        "id": "f88d973fbbb354a085cd6afc1f51d6b8",
                        "content": "<text hasMath=\"true\">$$\\Theta$$</text>"
                    },
                    {
                        "id": "226d7bf4e409e1a3eb45294821482498",
                        "content": "<text hasMath=\"true\">$$J(\\Theta)$$</text>"
                    },
                    {
                        "id": "137aeec19bde1d11a010b5307865f96e",
                        "content": "<text hasMath=\"true\">The (partial) derivative terms $$\\frac{\\partial}{\\partial\\Theta_{ij}^{(l)}}$$ for every $$i,j,l$$</text>"
                    },
                    {
                        "id": "7717402d51e3ecda8085870a30a0773a",
                        "content": "<text hasMath=\"true\">$$J(\\Theta)$$ and the (partial) derivative terms $$\\frac{\\partial}{\\partial\\Theta_{ij}^{(l)}}$$ for every $$i,j,l$$</text>"
                    }
                ],
                "answer": [
                    "7717402d51e3ecda8085870a30a0773a"
                ],
                "explanation": "",
                "videoCuePoint": 392500
            }
        ]
    },
    {
        "videoId": "Itp6fL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "853866b30fb844f960d86e3194e9e6ee",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you have two training examples $$(x^{(1)}, y^{(1)})$$ and $$(x^{(2)}, y^{(2)})$$. Which of the following is a correct sequence of operations for computing the gradient? (Below, FP = forward propagation, BP = back propagation).</text>",
                "options": [
                    {
                        "id": "c2b7c0a9d86c637debb2d1a7e891e394",
                        "content": "<text hasMath=\"true\">FP using $$x^{(1)}$$ followed by FP using $$x^{(2)}$$. Then BP using $$y^{(1)}$$ followed by BP using $$y^{(2)}$$.</text>"
                    },
                    {
                        "id": "ee2270ec406438a366c2aa3d0e1a53db",
                        "content": "<text hasMath=\"true\">FP using $$x^{(1)}$$ followed by BP using $$y^{(2)}$$. Then FP using $$x^{(2)}$$ followed by BP using $$y^{(1)}$$.</text>"
                    },
                    {
                        "id": "3e4ded68d7537653c862932580175843",
                        "content": "<text hasMath=\"true\">BP using $$y^{(1)}$$ followed by FP using $$x^{(1)}$$. Then BP using $$y^{(2)}$$ followed by FP using $$x^{(2)}$$.</text>"
                    },
                    {
                        "id": "944ae770279d8e287172e0a9e7beb8fe",
                        "content": "<text hasMath=\"true\">FP using $$x^{(1)}$$ followed by BP using $$y^{(1)}$$. Then FP using $$x^{(2)}$$ followed by BP using $$y^{(2)}$$.</text>"
                    }
                ],
                "answer": [
                    "944ae770279d8e287172e0a9e7beb8fe"
                ],
                "explanation": "",
                "videoCuePoint": 687600
            }
        ]
    },
    {
        "videoId": "Itrvrb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5e0df061f0f71b13980dc4008b1da09c",
                "type": "mcq",
                "definition": "<text>Consider the following neural network:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/9.3-quiz-1-q.png\" alt=\"A four layer neural network, with two units in each layer except for the output, which has one unit. There are full connections between layers. z_i^l, a_i^l, and delta_i^l are all defined as in lecture. Both connections coming out of the first non-bias unit in the second layer are red (and are 0).\" /><text hasMath=\"true\">Suppose both of the weights shown in red ($$\\Theta_{11}^{(2)}$$ and $$\\Theta_{21}^{(2)}$$) are equal to 0. After running backpropagation, what can we say about the value of $$\\delta_1^{(3)}$$?</text>",
                "options": [
                    {
                        "id": "94ec9cc91883276b32a01bbcd4d10348",
                        "content": "<text hasMath=\"true\">$$\\delta_1^{(3)} &gt; 0$$</text>"
                    },
                    {
                        "id": "972db283a2c4febee57eaacbfc02e3a7",
                        "content": "<text hasMath=\"true\">$$\\delta_1^{(3)} = 0$$ only if $$\\delta_1^{(2)} = \\delta_2^{(2)} = 0$$, but not necessarily otherwise</text>"
                    },
                    {
                        "id": "38339ec9aca75cc798b04c8f06100a7a",
                        "content": "<text hasMath=\"true\">$$\\delta_1^{(3)} \\leq 0$$ regardless of the values of $$\\delta_1^{(2)}$$ and $$\\delta_2^{(2)}$$</text>"
                    },
                    {
                        "id": "21e46ecd3a3383a50340ede88ea72107",
                        "content": "<text>There is insufficient information to tell</text>"
                    }
                ],
                "answer": [
                    "21e46ecd3a3383a50340ede88ea72107"
                ],
                "explanation": "",
                "videoCuePoint": 731800
            }
        ]
    },
    {
        "videoId": "Ittk3r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "6ab5d4ebdb0bbeeafec3bdec9ba4ec1a",
                "type": "mcq",
                "definition": "<text>Suppose D1 is a 10x6 matrix and D2 is a 1x11 matrix. You set:</text><text>DVec = [D1(:); D2(:)];</text><text>Which of the following would get D2 back from DVec?</text>",
                "options": [
                    {
                        "id": "b5c91e2a83d8436e68cdaf279069e305",
                        "content": "<text>reshape(DVec(60:71), 1, 11)</text>"
                    },
                    {
                        "id": "30086a0ec7dbc1ebdfe4f2adbed1b84f",
                        "content": "<text>reshape(DVec(61:72), 1, 11)</text>"
                    },
                    {
                        "id": "bc61c327d2ae88c98eb9ff38fbb1763b",
                        "content": "<text>reshape(DVec(61:71), 1, 11)</text>"
                    },
                    {
                        "id": "bbdc520fec98196be1d4e0f5688b6b1b",
                        "content": "<text>reshape(DVec(60:70), 11, 1)</text>"
                    }
                ],
                "answer": [
                    "bc61c327d2ae88c98eb9ff38fbb1763b"
                ],
                "explanation": "",
                "videoCuePoint": 227800
            }
        ]
    },
    {
        "videoId": "Ituy_71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "f72865cfcc4874aea29a54b67d8e6a03",
                "type": "mcq",
                "definition": "<text>What is the main reason that we use the backpropagation algorithm rather than the numerical gradient computation method during learning?</text>",
                "options": [
                    {
                        "id": "dd78cbcf769d351004db0a8610c51111",
                        "content": "<text>The numerical gradient computation method is much harder to implement.</text>"
                    },
                    {
                        "id": "7753ea1ae63f9391f13b0046bf8014dc",
                        "content": "<text>The numerical gradient algorithm is very slow.</text>"
                    },
                    {
                        "id": "c5e9ebb77866c69fae0e8d05d42fb873",
                        "content": "<text>Backpropagation does not require setting the parameter EPSILON.</text>"
                    },
                    {
                        "id": "7fa234364458198340fe265ac3eefddb",
                        "content": "<text>None of the above.</text>"
                    }
                ],
                "answer": [
                    "7753ea1ae63f9391f13b0046bf8014dc"
                ],
                "explanation": "",
                "videoCuePoint": 679700
            },
            {
                "id": "788d097e06b20a04302c9e3ec6e3bc76",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Let $$J(\\theta) = \\theta^3$$. Furthermore, let $$\\theta = 1$$ and $$\\epsilon = 0.01$$. You use the formula:</text><text hasMath=\"true\">$$\\frac{J(\\theta+\\epsilon) - J(\\theta - \\epsilon)}{2\\epsilon}$$</text><text hasMath=\"true\">to approximate the derivative. What value do you get using this approximation? (When $$\\theta = 1$$, the true, exact derivative is $$\\frac{d}{d\\theta}J(\\theta)=3$$).</text>",
                "options": [
                    {
                        "id": "892a8d84e1062a3de5347cbea80685f3",
                        "content": "<text>3.0000</text>"
                    },
                    {
                        "id": "b7210533750e903db44706849f2c5e8d",
                        "content": "<text>3.0001</text>"
                    },
                    {
                        "id": "d6c780503efcdd5725eeedc1b60da6e3",
                        "content": "<text>3.0301</text>"
                    },
                    {
                        "id": "4d546e22979e82c0ae437dd43c7e5a05",
                        "content": "<text>6.0002</text>"
                    }
                ],
                "answer": [
                    "b7210533750e903db44706849f2c5e8d"
                ],
                "explanation": "",
                "videoCuePoint": 301000
            }
        ]
    },
    {
        "videoId": "ItwBIL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5ebd5f3774e0d6895f9fec318ff9acfc",
                "type": "mcq",
                "definition": "<text>Consider this procedure for initializing the parameters of a neural network:</text><list bulletType=\"numbers\"><li><text>Pick a random number r = rand(1,1) * (2 * INIT_EPSILON) - INIT_EPSILON;</text></li><li><text hasMath=\"true\">Set $$\\Theta_{ij}^{(l)} = r$$ for all $$i,j,l$$.</text></li></list><text>Does this work?</text>",
                "options": [
                    {
                        "id": "64c917bfc1c5cf31b9e74327dc99c6ee",
                        "content": "<text>Yes, because the parameters are chosen randomly.</text>"
                    },
                    {
                        "id": "8859e7563b44ee3c73b6fa3fd553d5a5",
                        "content": "<text>Yes, unless we are unlucky and get r=0 (up to numerical precision).</text>"
                    },
                    {
                        "id": "6570021f35210efb21ebed26246af1a1",
                        "content": "<text>Maybe, depending on the training set inputs x(i).</text>"
                    },
                    {
                        "id": "f5ba1af83c74c9751896530383b652c0",
                        "content": "<text>No, because this fails to break symmetry.</text>"
                    }
                ],
                "answer": [
                    "f5ba1af83c74c9751896530383b652c0"
                ],
                "explanation": "",
                "videoCuePoint": 375600
            }
        ]
    },
    {
        "videoId": "ItzEcb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "dd268b567e7f90f1e60fad9403dbf415",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you are using gradient descent together with backpropagation to try to minimize $$J(\\Theta)$$ as a function of $$\\Theta$$. Which of the following would be a useful step for verifying that the learning algorithm is running correctly?</text>",
                "options": [
                    {
                        "id": "528b37ee8634ae8fad39e6f7c04b8e07",
                        "content": "<text hasMath=\"true\">Plot $$J(\\Theta)$$ as a function of $$\\Theta$$, to make sure gradient descent is going downhill.</text>"
                    },
                    {
                        "id": "10abdfecbe6d551884e9036382c4abdc",
                        "content": "<text hasMath=\"true\">Plot $$J(\\Theta)$$ as a function of the number of iterations and make sure it is increasing (or at least non-decreasing) with every iteration.</text>"
                    },
                    {
                        "id": "56113a4fa773f38c683928c718372da5",
                        "content": "<text hasMath=\"true\">Plot $$J(\\Theta)$$ as a function of the number of iterations and make sure it is decreasing (or at least non-increasing) with every iteration.</text>"
                    },
                    {
                        "id": "dbcc2e6a34067a103ee2e69e525ad460",
                        "content": "<text hasMath=\"true\">Plot $$J(\\Theta)$$ as a function of the number of iterations to make sure the parameter values are improving in classification accuracy.</text>"
                    }
                ],
                "answer": [
                    "56113a4fa773f38c683928c718372da5"
                ],
                "explanation": "",
                "videoCuePoint": 718600
            }
        ]
    },
    {
        "videoId": "It1gsr1-EeSqHiIAC2idzw",
        "questions": []
    },
    {
        "videoId": "It4kBL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "8453c64fbd2235bf2d6d633b52b5d44a",
                "type": "checkbox",
                "definition": "<text>Which of the following statements about diagnostics are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "dde531f324aa982012df66ccf03272cc",
                        "content": "<text>It\u2019s hard to tell what will work to improve a learning algorithm, so the best approach is to go with gut feeling and just see what works.</text>"
                    },
                    {
                        "id": "95cb8d86032be0d59667025b602b00dc",
                        "content": "<text>Diagnostics can give guidance as to what might be more fruitful things to try to improve a learning algorithm.</text>"
                    },
                    {
                        "id": "fbfea4fd3606cedf65e7bae82dc46038",
                        "content": "<text>Diagnostics can be time-consuming to implement and try, but they can still be a very good use of your time.</text>"
                    },
                    {
                        "id": "f744fb88acbeb88abb8a550cab3557ee",
                        "content": "<text>A diagnostic can sometimes rule out certain courses of action (changes to your learning algorithm) as being unlikely to improve its performance significantly.</text>"
                    }
                ],
                "answer": [
                    "95cb8d86032be0d59667025b602b00dc",
                    "fbfea4fd3606cedf65e7bae82dc46038",
                    "f744fb88acbeb88abb8a550cab3557ee"
                ],
                "explanation": "",
                "videoCuePoint": 331600
            }
        ]
    },
    {
        "videoId": "It6ZNb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "996e62712319fa725077861bcf6de041",
                "type": "mcq",
                "definition": "<text>Suppose an implementation of linear regression (without regularization) is badly overfitting the training set. In this case, we would expect:</text>",
                "options": [
                    {
                        "id": "8eae0f4e2afea3fab9c3088ec6c10c24",
                        "content": "<text hasMath=\"true\">The training error $$J(\\theta)$$ to be <strong>low</strong> and the test error $$J_{\\text{test}}(\\theta)$$ to be <strong>high</strong></text>"
                    },
                    {
                        "id": "30c0590a91578cfd85e073b008751713",
                        "content": "<text hasMath=\"true\">The training error $$J(\\theta)$$ to be <strong>low</strong> and the test error $$J_{\\text{test}}(\\theta)$$ to be <strong>low</strong></text>"
                    },
                    {
                        "id": "ee8600d01d542f2c6561365aea295498",
                        "content": "<text hasMath=\"true\">The training error $$J(\\theta)$$ to be <strong>high</strong> and the test error $$J_{\\text{test}}(\\theta)$$ to be <strong>low</strong></text>"
                    },
                    {
                        "id": "ec08dbd63e33f168efaf9c1699108c4e",
                        "content": "<text hasMath=\"true\">The training error $$J(\\theta)$$ to be <strong>high</strong> and the test error $$J_{\\text{test}}(\\theta)$$ to be <strong>high</strong></text>"
                    }
                ],
                "answer": [
                    "8eae0f4e2afea3fab9c3088ec6c10c24"
                ],
                "explanation": "",
                "videoCuePoint": 167600
            }
        ]
    },
    {
        "videoId": "It8OZr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "43dc4df04ba4d6f79d38f500e8f3fb28",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider the model selection procedure where we choose the degree of polynomial using a cross validation set. For the final model (with parameters $$\\theta$$), we might generally expect $$J_{\\text{CV}}(\\theta)$$ To be lower than $$J_\\text{test}(\\theta)$$ because:</text>",
                "options": [
                    {
                        "id": "2fe32e0164efa03aba209bc0eef3a914",
                        "content": "<text hasMath=\"true\">An extra parameter ($$d$$, the degree of the polynomial) has been fit to the cross validation set.</text>"
                    },
                    {
                        "id": "5b95b5d6668e6684253ed4cdada51250",
                        "content": "<text hasMath=\"true\">An extra parameter ($$d$$, the degree of the polynomial) has been fit to the test set.</text>"
                    },
                    {
                        "id": "3abc360a97da190535a22060d9149554",
                        "content": "<text>The cross validation set is usually smaller than the test set.</text>"
                    },
                    {
                        "id": "3a704dff3ef15259c7c78a683a3014b3",
                        "content": "<text>The cross validation set is usually larger than the test set.</text>"
                    }
                ],
                "answer": [
                    "2fe32e0164efa03aba209bc0eef3a914"
                ],
                "explanation": "",
                "videoCuePoint": 682700
            }
        ]
    },
    {
        "videoId": "It-qp71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "06f5eddcb9f676c856a65cedace93509",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you have a classification problem. The (misclassification) error is defined as $$\\frac{1}{m}\\sum_{i=1}^m\\text{err}(h_\\theta(x^{(i)}),y^{(i)})$$, and the cross validation (misclassification) error is similarly defined, using the cross validation examples $$(x_\\text{cv}^{(1)}, y_\\text{cv}^{(1)}),\\ldots,(x_\\text{cv}^{(m_\\text{cv})}, y_\\text{cv}^{(m_\\text{cv})})$$. Suppose your training error is 0.10, and your cross validation error is 0.30. What problem is the algorithm most likely to be suffering from?</text>",
                "options": [
                    {
                        "id": "98cf3a99139efc241a30316f1ff0269d",
                        "content": "<text>High bias (overfitting)</text>"
                    },
                    {
                        "id": "39792dd50b6f777f7500099f2792287d",
                        "content": "<text>High bias (underfitting)</text>"
                    },
                    {
                        "id": "55bfdb13decac83d5946f3e5db94acc7",
                        "content": "<text>High variance (overfitting)</text>"
                    },
                    {
                        "id": "6a060fabc7b56db4fac70c3c7672d746",
                        "content": "<text>High variance (underfitting)</text>"
                    }
                ],
                "answer": [
                    "55bfdb13decac83d5946f3e5db94acc7"
                ],
                "explanation": "",
                "videoCuePoint": 428000
            }
        ]
    },
    {
        "videoId": "IuBG6L1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "4ebf199126200af80ec064a05cac1d9a",
                "type": "mcq",
                "definition": "<text>Consider regularized logistic regression. Let</text><list bulletType=\"bullets\"><li><text hasMath=\"true\">$$J(\\theta) = \\frac{1}{2m}[\\sum_{i=1}^m(h_\\theta(x^{(i)})-y^{(i)})^2 + \\lambda\\sum_{j=2}^n \\theta_j^2]$$</text></li><li><text hasMath=\"true\">$$J_\\text{train}(\\theta) = \\frac{1}{2m_\\text{train}}[\\sum_{i=1}^{m_\\text{train}}(h_\\theta(x_\\text{train}^{(i)})-y_\\text{train}^{(i)})^2]$$</text></li><li><text hasMath=\"true\">$$J_\\text{CV}(\\theta) = \\frac{1}{2m_\\text{CV}}[\\sum_{i=1}^{m_\\text{CV}}(h_\\theta(x_\\text{CV}^{(i)})-y_\\text{CV}^{(i)})^2]$$</text></li></list><text hasMath=\"true\">Suppose you plot $$J_\\text{train}$$ and $$J_\\text{CV}$$ as a function of the regularization parameter $$\\lambda$$. which of the following plots do you expect to get?</text>",
                "options": [
                    {
                        "id": "57086c57128f8a260b964127970cfeec",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/10.5-quiz-1-option1.png\" alt=\"J_train at first decreases as a function of lambda, but then increases. J_CV continually decreases as a function of lambda. J_CV is lower than J_train.\" />"
                    },
                    {
                        "id": "55abdb92021173b330bc324340cb6659",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/10.5-quiz-1-option2.png\" alt=\"J_train at first decreases as a function of lambda, but then increases. J_CV continually increases as a function of lambda. J_CV is lower than J_train.\" />"
                    },
                    {
                        "id": "68cbc00bf5c9eabfd9da3f7e831316cb",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/10.5-quiz-1-option3.png\" alt=\"J_train  continually decreases as a function of lambda. J_CV at first decreases as a function of lambda, but then increases. J_CV is higher than J_train.\" />"
                    },
                    {
                        "id": "9ec9e6d467869acbc19d54e2398ca371",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/10.5-quiz-1-option4.png\" alt=\"J_train  continually increases as a function of lambda. J_CV at first decreases as a function of lambda, but then increases. J_CV is higher than J_train.\" />"
                    }
                ],
                "answer": [
                    "9ec9e6d467869acbc19d54e2398ca371"
                ],
                "explanation": "",
                "videoCuePoint": 467600
            }
        ]
    },
    {
        "videoId": "IuC8Gb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "88b382f2af1e18a65d67427c44d9f50c",
                "type": "checkbox",
                "definition": "<text>In which of the following circumstances is getting more training data likely to significantly help a learning algorithm\u2019s performance? </text>",
                "options": [
                    {
                        "id": "3aaba8a59d3226db46cf18d46bf3cd1e",
                        "content": "<text>Algorithm is suffering from high bias.</text>"
                    },
                    {
                        "id": "e157413e5ed19233e5f5fc1c9581c0e4",
                        "content": "<text>Algorithm is suffering from high variance.</text>"
                    },
                    {
                        "id": "38bf6d197f3d479479dbe2bafec096f4",
                        "content": "<text hasMath=\"true\">$$J_\\text{CV}(\\theta)$$ (cross validation error) is much larger than $$J_\\text{train}(\\theta)$$ (training error).</text>"
                    },
                    {
                        "id": "6e40549088ec8b3ffd9769a5e9f6fb83",
                        "content": "<text hasMath=\"true\">$$J_\\text{CV}(\\theta)$$ (cross validation error) is about the same as $$J_\\text{train}(\\theta)$$ (training error).</text>"
                    }
                ],
                "answer": [
                    "e157413e5ed19233e5f5fc1c9581c0e4",
                    "38bf6d197f3d479479dbe2bafec096f4"
                ],
                "explanation": "",
                "videoCuePoint": 703700
            }
        ]
    },
    {
        "videoId": "IuK36r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "cccf380367a84a6e2f8ed71153bf2b2d",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you fit a neural network with one hidden layer to a training set. You find that the cross validation error $$J_\\text{CV}(\\theta)$$ is much larger than the training error $$J_\\text{train}(\\theta)$$. Is increasing the number of hidden units likely to help?</text>",
                "options": [
                    {
                        "id": "cdfc775b22cb291e17934e5a11af32f8",
                        "content": "<text>Yes, because this increases the number of parameters and lets the network represent more complex functions.</text>"
                    },
                    {
                        "id": "3af89e1e2e56b6db6c262c53520a9b07",
                        "content": "<text>Yes, because it is currently suffering from high bias.</text>"
                    },
                    {
                        "id": "aa2322f0601f735a34e448452f7415c1",
                        "content": "<text>No, because it is currently suffering from high bias, so adding hidden units is unlikely to help.</text>"
                    },
                    {
                        "id": "5334f465602b460e5775d5e16ae4cf68",
                        "content": "<text>No, because it is currently suffering from high variance, so adding hidden units is unlikely to help.</text>"
                    }
                ],
                "answer": [
                    "5334f465602b460e5775d5e16ae4cf68"
                ],
                "explanation": "",
                "videoCuePoint": 361800
            }
        ]
    },
    {
        "videoId": "IuPwa71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "48eea7bb4e2d62179c977be378915129",
                "type": "checkbox",
                "definition": "<text>Which of the following statements do you agree with? Check all that apply.</text>",
                "options": [
                    {
                        "id": "94639876db3409caadb22241ade174e1",
                        "content": "<text>For some learning applications, it is possible to imagine coming up with many different features (e.g. email body features, email routing features, etc.). But it can be hard to guess in advance which features will be the most helpful.</text>"
                    },
                    {
                        "id": "4c18ac20408d0090b1661ffd63cec44b",
                        "content": "<text>For spam classification, algorithms to detect and correct deliberate misspellings will make a significant improvement in accuracy.</text>"
                    },
                    {
                        "id": "82c3fbad15ca52f28af9a7b96babd472",
                        "content": "<text>Because spam classification uses very high dimensional feature vectors (e.g. n = 50,000 if the features capture the presence or absence of 50,000 different words), a significant effort to collect a massive training set will always be a good idea.</text>"
                    },
                    {
                        "id": "03d655929baddc061340853f9f00744d",
                        "content": "<text>There are often many possible ideas for how to develop a high accuracy learning system; \u201cgut feeling\u201d is not a recommended way to choose among the alternatives.</text>"
                    }
                ],
                "answer": [
                    "94639876db3409caadb22241ade174e1",
                    "03d655929baddc061340853f9f00744d"
                ],
                "explanation": "",
                "videoCuePoint": 467700
            }
        ]
    },
    {
        "videoId": "IuSMrL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "adecb4e71876ba4196d62b16f3c9edfc",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Why is the recommended approach to perform error analysis using the cross validation data used to compute $$J_\\text{CV}(\\theta)$$ rather than the test data used to compute $$J_\\text{test}(\\theta)$$?</text>",
                "options": [
                    {
                        "id": "c468e2e672105eda9003fcd20ec0169d",
                        "content": "<text>The cross validation data set is usually large.</text>"
                    },
                    {
                        "id": "c4aa02059540060c56156c0a2be248d4",
                        "content": "<text>This process will give a lower error on the test set.</text>"
                    },
                    {
                        "id": "793dcb560e68eb29575e37b11128f3bb",
                        "content": "<text>If we develop new features by examining the test set, then we may end up choosing features that work well specifically for the test set, so Jtest(\u03b8) is no longer a good estimate of how well we generalize to new examples.</text>"
                    },
                    {
                        "id": "7e7744a4a9be5fdf2cc7985a7f60da15",
                        "content": "<text>Doing so is less likely to lead to choosing an excessive number of features.</text>"
                    }
                ],
                "answer": [
                    "793dcb560e68eb29575e37b11128f3bb"
                ],
                "explanation": "",
                "videoCuePoint": 546800
            }
        ]
    },
    {
        "videoId": "IuUB3b1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e40e45b5e17cac9140074e2fa42443d7",
                "type": "mcq",
                "definition": "<text>Precision and recall are defined according to:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/11.3-quiz-1-q1.png\" alt=\"If predicted class and actual class are both 1, then a test example is a True Positive. If predicted class and actual class are both 0, then a test example is a True Negative. If predicted class is 0 actual class is 1, then a test example is a False Negative. If predicted class is 1 and actual class is 0, then a test example is a False Positive.\" /><text hasMath=\"true\">$$\\text{Precision} = \\frac{\\text{True positives}}{\\text{# predicted as positive}} = \\frac{\\text{True positives}}{\\text{True positives + False positives}}$$</text><text hasMath=\"true\">$$\\text{Recall} = \\frac{\\text{True positives}}{\\text{# actual positives}} = \\frac{\\text{True positives}}{\\text{True positives + False negatives}}$$</text><text>Your algorithm\u2019s performance on the test set is given to the right. What is the algorithm\u2019s recall?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/11.3-quiz-1-q2.png\" alt=\"80 examples had actual class 1 and predicted class 1. 20 examples had actual class 0 and predicted class 1. 80 examples had actual class 1 and predicted class 0. 820 examples had actual class 0 and predicted class 0.\" />",
                "options": [
                    {
                        "id": "6b8db1f90430bceaef148b0dc8dc077d",
                        "content": "<text>0.5</text>"
                    },
                    {
                        "id": "550b9d89e1d60f9e27cf1098812789fd",
                        "content": "<text>0.8</text>"
                    },
                    {
                        "id": "8ff0b7716133fc46b4d0d5bcb098cc51",
                        "content": "<text>0.08</text>"
                    },
                    {
                        "id": "eda7d6cad393a7b0cfaec0b371971b81",
                        "content": "<text>0.1</text>"
                    }
                ],
                "answer": [
                    "6b8db1f90430bceaef148b0dc8dc077d"
                ],
                "explanation": "",
                "videoCuePoint": 585700
            },
            {
                "id": "b7097a8d95c85a841144cc650f27ae8a",
                "type": "mcq",
                "definition": "<text>Precision and recall are defined according to:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/11.3-quiz-1-q1.png\" alt=\"If predicted class and actual class are both 1, then a test example is a True Positive. If predicted class and actual class are both 0, then a test example is a True Negative. If predicted class is 0 actual class is 1, then a test example is a False Negative. If predicted class is 1 and actual class is 0, then a test example is a False Positive.\" /><text hasMath=\"true\">$$\\text{Precision} = \\frac{\\text{True positives}}{\\text{# predicted as positive}} = \\frac{\\text{True positives}}{\\text{True positives + False positives}}$$</text><text hasMath=\"true\">$$\\text{Recall} = \\frac{\\text{True positives}}{\\text{# actual positives}} = \\frac{\\text{True positives}}{\\text{True positives + False negatives}}$$</text><text>Your algorithm\u2019s performance on the test set is given to the right. What is the algorithm\u2019s precision?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/11.3-quiz-1-q2.png\" alt=\"80 examples had actual class 1 and predicted class 1. 20 examples had actual class 0 and predicted class 1. 80 examples had actual class 1 and predicted class 0. 820 examples had actual class 0 and predicted class 0.\" />",
                "options": [
                    {
                        "id": "68475f1cedbfc15f1bfa7c473df74602",
                        "content": "<text>0.8</text>"
                    },
                    {
                        "id": "17ef60659bac8c81b108937a9f6582b4",
                        "content": "<text>0.5</text>"
                    },
                    {
                        "id": "93805748627446899cd25489b671f754",
                        "content": "<text>0.08</text>"
                    },
                    {
                        "id": "f3c4c5186fb1fd12cc842dc54826880f",
                        "content": "<text>0.1</text>"
                    }
                ],
                "answer": [
                    "68475f1cedbfc15f1bfa7c473df74602"
                ],
                "explanation": "",
                "videoCuePoint": 585700
            }
        ]
    },
    {
        "videoId": "IuWeHr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "42dbfd679204cd5962aef51e17aa6fc7",
                "type": "mcq",
                "definition": "<text>You have trained a logistic regression classifier and plan to make predictions according to:</text><list bulletType=\"bullets\"><li><text hasMath=\"true\">Predict $$y = 1$$ if $$h_\\theta(x) \\geq \\text{threshold}$$</text></li><li><text hasMath=\"true\">Predict $$y = 0$$ if $$h_\\theta(x) &lt; \\text{threshold}$$</text></li></list><text>For different values of the threshold parameter, you get different values of precision (P) and recall (R). Which of of the following would be a reasonable way to pick the value to use for the threshold?</text>",
                "options": [
                    {
                        "id": "295a045ac6b0f155d0609a5b22ee4c1f",
                        "content": "<text hasMath=\"true\">Measure precision (P) and recall (R) on the <strong>test set</strong> and choose the value of threshold which maximizes $$\\frac{P+R}{2}$$</text>"
                    },
                    {
                        "id": "a89ab5b57ab32356f2e0fe02fb76f5c9",
                        "content": "<text hasMath=\"true\">Measure precision (P) and recall (R) on the <strong>test set</strong> and choose the value of threshold which maximizes $$2\\frac{PR}{P+R}$$</text>"
                    },
                    {
                        "id": "6df2336cc181c9281c26a9073c6ce9dd",
                        "content": "<text hasMath=\"true\">Measure precision (P) and recall (R) on the <strong>cross validation set</strong> and choose the value of threshold which maximizes $$\\frac{P+R}{2}$$</text>"
                    },
                    {
                        "id": "b63add9dc264d3513b3e8ed5606229c1",
                        "content": "<text hasMath=\"true\">Measure precision (P) and recall (R) on the <strong>cross validation set</strong> and choose the value of threshold which maximizes $$2\\frac{PR}{P+R}$$</text>"
                    }
                ],
                "answer": [
                    "b63add9dc264d3513b3e8ed5606229c1"
                ],
                "explanation": "",
                "videoCuePoint": 779600
            }
        ]
    },
    {
        "videoId": "IuYTT71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "ec298f2c4835d4bd5e4b448f35f997d2",
                "type": "checkbox",
                "definition": "<text>Having a large training set can help significantly improve a learning algorithm\u2019s performance. However, the large training set is <strong>unlikely</strong> to help when:</text>",
                "options": [
                    {
                        "id": "65869cc148cc5862b88f7b0f5e24e374",
                        "content": "<text>The features x do not contain enough information to predict y accurately (such as predicting a house\u2019s price from only its size), and we are using a simple learning algorithm such as logistic regression.</text>"
                    },
                    {
                        "id": "41b4685cc202191a83e7d8473a8ead96",
                        "content": "<text>We are using a learning algorithm with a large number of features (i.e. one with \u201clow bias\u201d).</text>"
                    },
                    {
                        "id": "4e4ef60881402bc27a1847a8224f5083",
                        "content": "<text>The features x do not contain enough information to predict y accurately (such as predicting a house\u2019s price from only its size), even if we are using a neural network with a large number of hidden units.</text>"
                    },
                    {
                        "id": "bb021a452f911d9016d371f3b6d9e601",
                        "content": "<text>We are not using regularization (e.g. the regularization parameter \u03bb = 0).</text>"
                    }
                ],
                "answer": [
                    "65869cc148cc5862b88f7b0f5e24e374",
                    "4e4ef60881402bc27a1847a8224f5083"
                ],
                "explanation": "",
                "videoCuePoint": 626700
            }
        ]
    },
    {
        "videoId": "IuavkL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e3f604653c20f799729127dc8fbb6746",
                "type": "mcq",
                "definition": "<text>Consider the following minimization problems:</text><list bulletType=\"numbers\"><li><text hasMath=\"true\">$$\\displaystyle\\mathop{\\mbox{min}}_\\theta\\ \\frac{1}{m}\\left[\\sum_{i=1}^{m}y^{(i)}\\text{cost}_1(\\theta^Tx^{(i)}) + (1-y^{(i)}) \\text{cost}_0(\\theta^Tx^{(i)})\\right]+\\frac{\\lambda}{2m}\\sum_{j=1}^n\\theta^2_j$$</text></li><li><text hasMath=\"true\">$$\\displaystyle\\mathop{\\mbox{min}}_\\theta\\ C\\left[\\sum_{i=1}^{m}y^{(i)}\\text{cost}_1(\\theta^Tx^{(i)}) + (1-y^{(i)}) \\text{cost}_0(\\theta^Tx^{(i)})\\right]+\\frac{1}{2}\\sum_{j=1}^n\\theta^2_j$$</text></li></list><text hasMath=\"true\">These two optimization problems will give the same value of $$\\theta$$ (i.e., the same value of $$\\theta$$ gives the optimal solution to both problems) if:</text>",
                "options": [
                    {
                        "id": "60b46f56e7f2cbc0b0c0f84e7e04f37c",
                        "content": "<text hasMath=\"true\">$$C = \\lambda$$</text>"
                    },
                    {
                        "id": "70f053751520d1453543e2c1ab2e15d9",
                        "content": "<text hasMath=\"true\">$$C = -\\lambda$$</text>"
                    },
                    {
                        "id": "466faf4513dab29f779388467d9d4125",
                        "content": "<text hasMath=\"true\">$$C = \\frac{1}{\\lambda}$$</text>"
                    },
                    {
                        "id": "354e0373c86a174e5744b4c6f43fcbce",
                        "content": "<text hasMath=\"true\">$$C = \\frac{2}{\\lambda}$$</text>"
                    }
                ],
                "answer": [
                    "466faf4513dab29f779388467d9d4125"
                ],
                "explanation": "",
                "videoCuePoint": 831600
            }
        ]
    },
    {
        "videoId": "IudL0b1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "427782b523e9c4b98e60f9830790e136",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider the training set to the right, where \"x\" denotes positive examples ($$y=1$$) and \"o\" denotes negative examples ($$y=0$$). Suppose you train an SVM (which will predict 1 when $$\\theta_0 + \\theta_1x_1 + \\theta_2x_2 \\geq 0$$). What values might the SVM give for $$\\theta_0$$, $$\\theta_1$$, and $$\\theta_2$$?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.2-quiz-1-q.png\" alt=\"red x\" />",
                "options": [
                    {
                        "id": "2d49dd98f3590f9894ebc34c1a58de96",
                        "content": "<text hasMath=\"true\">$$\\theta_0=3,\\theta_1=1,\\theta_2=0$$</text>"
                    },
                    {
                        "id": "3f936da787036aff371085a3d770cb12",
                        "content": "<text hasMath=\"true\">$$\\theta_0=-3,\\theta_1=1,\\theta_2=0$$</text>"
                    },
                    {
                        "id": "0dd7ec3859ecf42a94796b4c8b8d41d4",
                        "content": "<text hasMath=\"true\">$$\\theta_0=3,\\theta_1=0,\\theta_2=1$$</text>"
                    },
                    {
                        "id": "5c94edb9306f1388d19b854416bb3603",
                        "content": "<text hasMath=\"true\">$$\\theta_0=-3,\\theta_1=0,\\theta_2=1$$</text>"
                    }
                ],
                "answer": [
                    "3f936da787036aff371085a3d770cb12"
                ],
                "explanation": "",
                "videoCuePoint": 432600
            }
        ]
    },
    {
        "videoId": "IueZ8r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "de2eaa1e18062a97c1877d7db640d51c",
                "type": "mcq",
                "definition": "<text>The SVM optimization problem we used is:</text><text> </text><text hasMath=\"true\">$$\\begin{align*} \\min_\\theta &amp; \\frac{1}{2}\\sum_{j=1}^n\\theta_j^2\\\\ \\mbox{s.t.} &amp; \\|\\theta\\|\\cdot p^{(i)} \\geq 1\\quad \\mbox{if}\\ y^{(i)} = 1\\\\ &amp; \\|\\theta\\|\\cdot p^{(i)} \\leq -1\\quad \\mbox{if}\\ y^{(i)} = 0 \\end{align*}$$</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.3-quiz-1-q.png\" alt=\"\" /><text hasMath=\"true\">where $$p^{(i)}$$ is the (signed - positive or negative) projection of $$x^{(i)}$$ onto $$\\theta$$. Consider the training set above. At the optimal value of $$\\theta$$, what is $$\\|\\theta\\|$$?</text><text />",
                "options": [
                    {
                        "id": "8da878576d10f6432a7d8553bf5bdc95",
                        "content": "<text>1/4</text>"
                    },
                    {
                        "id": "8884a8ef717721f09e36d7ce86f4f546",
                        "content": "<text>1/2</text>"
                    },
                    {
                        "id": "2339105d54c5f7e6432587597672ce3e",
                        "content": "<text>1</text>"
                    },
                    {
                        "id": "f22bb3f1f680395f3a74bac61beec35e",
                        "content": "<text>2</text>"
                    }
                ],
                "answer": [
                    "8884a8ef717721f09e36d7ce86f4f546"
                ],
                "explanation": "",
                "videoCuePoint": 1166800
            }
        ]
    },
    {
        "videoId": "IugPI71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "k4pyPrLrEeSTXyIACzQGuw@8",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Consider a 1-D example with one feature $$x_1$$. Suppose $$l^{(1)}=5$$. To the right is a plot of $$f_1 = \\exp(-\\frac{\\|x_1-l^{(1)}\\|}{2\\sigma^2})$$ when $$\\sigma^2 = 1$$. Suppose we now change $$\\sigma^2=4$$. Which of the following is a plot of $$f_1$$ with the new value of $$\\sigma^2$$?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.4-quiz-1-q.png\" alt=\"A plot of a Gaussian kernel centered at 5. It has a peak at (5,1).\" />",
                "options": [
                    {
                        "id": "de0daa3cae15758e7370f5e1cc7f6c79",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.4-quiz-1-option1.png\" />"
                    },
                    {
                        "id": "42fe76bee775e16529c7547f214eca27",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.4-quiz-1-option2.png\" />"
                    },
                    {
                        "id": "2f3da90ca23c6fff8cfeb1dde405016f",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.4-quiz-1-option3.png\" />"
                    },
                    {
                        "id": "58f30a00516134d312c5dd7a0326b1fe",
                        "content": "<img src=\"http://spark-public.s3.amazonaws.com/ml/images/12.4-quiz-1-option4.png\" />"
                    }
                ],
                "answer": [
                    "2f3da90ca23c6fff8cfeb1dde405016f"
                ],
                "explanation": "",
                "videoCuePoint": 662800
            }
        ]
    },
    {
        "videoId": "IuhdRL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "03056cf0f92ee5e4c590ad299dc6afa5",
                "type": "checkbox",
                "definition": "<text>Suppose you train an SVM and find it overfits your training data. Which of these would be a reasonable next step? Check all that apply.</text>",
                "options": [
                    {
                        "id": "0b29d5b1a19fe4505fa6a7d8c3dc464b",
                        "content": "<text hasMath=\"true\">Increase $$C$$</text>"
                    },
                    {
                        "id": "04f297f7deedfb79a30fe804ea6b5c92",
                        "content": "<text hasMath=\"true\">Decrease $$C$$</text>"
                    },
                    {
                        "id": "f1d5ce954ce4269c8314b26f2df06565",
                        "content": "<text hasMath=\"true\">Increase $$\\sigma^2$$</text>"
                    },
                    {
                        "id": "f3a2bf7babc444a9cfcc4a278dde1d42",
                        "content": "<text hasMath=\"true\">Decrease $$\\sigma^2$$</text>"
                    }
                ],
                "answer": [
                    "04f297f7deedfb79a30fe804ea6b5c92",
                    "f1d5ce954ce4269c8314b26f2df06565"
                ],
                "explanation": "",
                "videoCuePoint": 931400
            }
        ]
    },
    {
        "videoId": "Iukglb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "49290bcbee8d16b1607477327003ebc6",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you are trying to decide among a few different choices of kernel and are also choosing parameters such as $$C$$, $$\\sigma^2$$, etc. How should you make the choice?</text>",
                "options": [
                    {
                        "id": "42a906fc1d164522571549dc9c37f80e",
                        "content": "<text>Choose whatever performs best on the training data.</text>"
                    },
                    {
                        "id": "57ccde0cb54203485457768f8213bdb0",
                        "content": "<text>Choose whatever performs best on the cross-validation data.</text>"
                    },
                    {
                        "id": "f8bf2ef55139339704c51629daff40fd",
                        "content": "<text>Choose whatever performs best on the test data.</text>"
                    },
                    {
                        "id": "45f02924c14859b6a65f9ff3f1ba5dc1",
                        "content": "<text>Choose whatever gives the largest SVM margin.</text>"
                    }
                ],
                "answer": [
                    "57ccde0cb54203485457768f8213bdb0"
                ],
                "explanation": "",
                "videoCuePoint": 770700
            }
        ]
    },
    {
        "videoId": "Ium81r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "df496a202d6056f7f8cfe39756a0cec0",
                "type": "checkbox",
                "definition": "<text>Which of the following statements are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "2ca77674db44db21267b619bb2476b52",
                        "content": "<text hasMath=\"true\">In unsupervised learning, the training set is of the form $$\\{x^{(1)},x^{(2)},\\dots,x^{(m)}\\}$$ without labels $$y^{(i)}$$.</text>"
                    },
                    {
                        "id": "34f6d05717360da28427817333e6f122",
                        "content": "<text>Clustering is an example of unsupervised learning.</text>"
                    },
                    {
                        "id": "5139902c72df95f2a40b2eb88629bbe0",
                        "content": "<text>In unsupervised learning, you are given an unlabeled dataset and are asked to find \"structure\" in the data.</text>"
                    },
                    {
                        "id": "d8ba863c1bafb64ef5820e01f85db2b5",
                        "content": "<text>Clustering is the only unsupervised learning algorithm.</text>"
                    }
                ],
                "answer": [
                    "2ca77674db44db21267b619bb2476b52",
                    "34f6d05717360da28427817333e6f122",
                    "5139902c72df95f2a40b2eb88629bbe0"
                ],
                "explanation": "",
                "videoCuePoint": 185000
            }
        ]
    },
    {
        "videoId": "IuoyB71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "f9ab666752e11d78a8619021194549d0",
                "type": "checkbox",
                "definition": "<text hasMath=\"true\">Suppose you run k-means and after the algorithm converges, you have: $$c^{(1)} = 3, c^{(2)} = 3, c^{(3)} = 5, \\dots$$</text><text>Which of the following statements are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "3e717e2a4f623c9fc3ba0a92cb4dce9c",
                        "content": "<text hasMath=\"true\">The third example $$x^{(3)}$$ has been assigned to cluster 5.</text>"
                    },
                    {
                        "id": "b803a0332ca8a59bdd5011eb015b1bcf",
                        "content": "<text hasMath=\"true\">The first and second training examples $$x^{(1)}$$ and $$x^{(2)}$$ have been assigned to the same cluster.</text>"
                    },
                    {
                        "id": "786f5514ed758495f2cd2cca51a13f41",
                        "content": "<text>The second and third training examples have been assigned to the same cluster.</text>"
                    },
                    {
                        "id": "149fbd681fc58b04735e3df64c33bff5",
                        "content": "<text hasMath=\"true\">Out of all the possible values of $$k\\in\\{1,2,\\dots,K\\}$$ the value $$k=3$$ minimizes $$\\|x^{(2)}-\\mu_k\\|^2$$.</text>"
                    }
                ],
                "answer": [
                    "3e717e2a4f623c9fc3ba0a92cb4dce9c",
                    "b803a0332ca8a59bdd5011eb015b1bcf",
                    "149fbd681fc58b04735e3df64c33bff5"
                ],
                "explanation": "",
                "videoCuePoint": 432600
            }
        ]
    },
    {
        "videoId": "IuqAKL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "ef0b1aa37c40794830ec90d7563b729e",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you have implemented k-means and to check that it is running correctly, you plot the cost function $$J(c^{(1)}, \\dots, c^{(m)}, \\mu_1, \\dots, \\mu_k)$$ as a function of the number of iterations. Your plot looks like this:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/14.3-quiz-1-q.png\" alt=\"The cost function is bumpy but trends downward\" /><text>What does this mean?</text>",
                "options": [
                    {
                        "id": "c3d98b168750a286719ed326dd1fe1ea",
                        "content": "<text>The learning rate is too large.</text>"
                    },
                    {
                        "id": "8da19d2850396b87d760d547f6e3d448",
                        "content": "<text>The algorithm is working correctly.</text>"
                    },
                    {
                        "id": "539fad846a3f6ac0e32f5596c4b73e4f",
                        "content": "<text hasMath=\"true\">The algorithm is working, but $$k$$ is too large.</text>"
                    },
                    {
                        "id": "db8ba2b5091409abafd94f9252480f34",
                        "content": "<text>It is not possible for the cost function to sometimes increase. There must be a bug in the code.</text>"
                    }
                ],
                "answer": [
                    "db8ba2b5091409abafd94f9252480f34"
                ],
                "explanation": "",
                "videoCuePoint": 384700
            }
        ]
    },
    {
        "videoId": "Iur1Wb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "b382af52e6ef81b269fe991d1c612da8",
                "type": "mcq",
                "definition": "<text>Which of the following is the recommended way to initialize k-means?</text>",
                "options": [
                    {
                        "id": "d5642146bf860968a9efb9e0e48c80cb",
                        "content": "<text hasMath=\"true\">Pick a random integer $$i$$ from $$\\{1,\\dots,k\\}$$. Set $$\\mu_1 = \\mu_2 = \\dots = \\mu_k = x^{(i)}$$.</text>"
                    },
                    {
                        "id": "fe30488f01094a3a063515ac7fc5d257",
                        "content": "<text hasMath=\"true\">Pick $$k$$ distinct random integers $$i_1, \\dots, i_k$$ from $$\\{1, \u2026, k\\}$$.</text><text hasMath=\"true\">Set $$\\mu_1 = x^{(i_1)}, \\mu_2 = x^{(i_2)}, \\dots, \\mu_k = x^{(i_k)}$$.</text>"
                    },
                    {
                        "id": "8132372dd4d8e18f18105068153a6f49",
                        "content": "<text hasMath=\"true\">Pick $$k$$ distinct random integers $$i_1, \\dots, i_k$$ from $$\\{1, \u2026, m\\}$$.</text><text hasMath=\"true\">Set $$\\mu_1 = x^{(i_1)}, \\mu_2 = x^{(i_2)}, \\dots, \\mu_k = x^{(i_k)}$$.</text>"
                    },
                    {
                        "id": "6a7dbdd6da07aaf9534f7d5a8750abb1",
                        "content": "<text hasMath=\"true\">Set every element of $$\\mu_i\\in\\mathbb{R}^n$$ to a random value between $$\u2013\\epsilon$$ and $$\\epsilon$$, for some small $$\\epsilon$$.</text>"
                    }
                ],
                "answer": [
                    "8132372dd4d8e18f18105068153a6f49"
                ],
                "explanation": "",
                "videoCuePoint": 440700
            }
        ]
    },
    {
        "videoId": "IutDer1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "9d27e978bceaf129e6cec8eea85c4902",
                "type": "mcq",
                "definition": "<text>Suppose you run k-means using k = 3 and k = 5. You find that the cost function J is much higher for k = 5 than for k = 3. What can you conclude?</text>",
                "options": [
                    {
                        "id": "37314183ddc4627351c238872854dcfe",
                        "content": "<text>This is mathematically impossible. There must be a bug in the code.</text>"
                    },
                    {
                        "id": "81044d75f804fa370848bf0f71917c0d",
                        "content": "<text>The correct number of clusters is k = 3.</text>"
                    },
                    {
                        "id": "edb5875df857f91166925f9a4a9cdb88",
                        "content": "<text>In the run with k = 5, k-means got stuck in a bad local minimum. You should try re-running k-means with multiple random initializations. </text>"
                    },
                    {
                        "id": "6a17bfb21944d8fa08eac84e83fbb160",
                        "content": "<text>In the run with k = 3, k-means got lucky. You should try re-running k-means with k = 3 and different random initializations until it performs no better than with k = 5.</text>"
                    }
                ],
                "answer": [
                    "edb5875df857f91166925f9a4a9cdb88"
                ],
                "explanation": "",
                "videoCuePoint": 269500
            }
        ]
    },
    {
        "videoId": "IuxU671-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "571e8aedb209d3427af2e2ce719e8f1f",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose we apply dimensionality reduction to a dataset of m examples $$\\{x^{(1)}, x^{(2)}, \\dots, x^{(m)}\\}$$, where $$x^{(i)}\\in\\mathbb{R}^n$$. As a result of this, we will get out:</text>",
                "options": [
                    {
                        "id": "8909be026d72106447084800b11b1f26",
                        "content": "<text hasMath=\"true\">A lower dimensional dataset $$\\{z^{(1)}, z^{(2)},\\dots, z^{(k)}\\}$$ of k examples where $$k\\leq n$$.  </text>"
                    },
                    {
                        "id": "ae7eb180a5ecbed266ed551980e92172",
                        "content": "<text hasMath=\"true\">A lower dimensional dataset $$\\{z^{(1)}, z^{(2)},\\dots, z^{(k)}\\}$$ of k examples where $$k &gt; n$$.  </text>"
                    },
                    {
                        "id": "78829d6c1f972eb6a1e177c571bd1a5f",
                        "content": "<text hasMath=\"true\">A lower dimensional dataset $$\\{z^{(1)}, z^{(2)},\\dots, z^{(m)}\\}$$ of m examples where $$z^{(i)} \\in \\mathbb{R}^k$$ for some value of $$k$$ and $$k\\leq n$$.  </text>"
                    },
                    {
                        "id": "065acbc00fd1dd8e1956ed8f33f4490b",
                        "content": "<text hasMath=\"true\">A lower dimensional dataset $$\\{z^{(1)}, z^{(2)},\\dots, z^{(m)}\\}$$ of m examples where $$z^{(i)} \\in \\mathbb{R}^k$$ for some value of $$k$$ and $$k &gt; n$$.  </text>"
                    }
                ],
                "answer": [
                    "78829d6c1f972eb6a1e177c571bd1a5f"
                ],
                "explanation": "",
                "videoCuePoint": 587700
            }
        ]
    },
    {
        "videoId": "IuzKHL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "377314c298bb912f68760cd07b0658fb",
                "type": "checkbox",
                "definition": "<text hasMath=\"true\">Suppose you have a dataset $$\\{x^{(1)}, x^{(2)}, \\dots, x^{(m)}\\}$$ where $$x^{(i)}\\in\\mathbb{R}^n$$. In order to visualize it, we apply dimensionality reduction and get $$\\{z^{(1)}, z^{(2)}, \\dots, z^{(m)}\\}$$ where $$z^{(i)}\\in\\mathbb{R}^k$$ is k-dimensional. In a typical setting, which of the following would you expect to be true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "23def20340b6cd5d82bd9ad21749a99a",
                        "content": "<text>k &gt; n</text>"
                    },
                    {
                        "id": "ab93a69a35b8f9d08762cbf72b0ba68e",
                        "content": "<text>k \u2264 n</text>"
                    },
                    {
                        "id": "55d84d2e0f3fd4de052c82af8c74e1dd",
                        "content": "<text>k \u2265 4</text>"
                    },
                    {
                        "id": "d2b4eed1d166a267c39369abb0ed05b3",
                        "content": "<text>k = 2 or k = 3 (since we can plot 2D or 3D data but don\u2019t have ways to visualize higher dimensional data)</text>"
                    }
                ],
                "answer": [
                    "ab93a69a35b8f9d08762cbf72b0ba68e",
                    "d2b4eed1d166a267c39369abb0ed05b3"
                ],
                "explanation": "",
                "videoCuePoint": 300600
            }
        ]
    },
    {
        "videoId": "Iu0_Tb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "7df1109f26725ab15a3091df604dc981",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Suppose you run PCA on the dataset below. Which of the following would be a reasonable vector $$u^{(1)}$$ onto which to project the data? (By convention, we choose $$u^{(1)}$$ so that $$\\|u^{(1)}\\| = \\sqrt{(u^{(1)}_1)^2 + (u^{(1)}_2)^2}$$, the length of the vector $$u^{(1)}$$, equals 1.)</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/15.3-quiz-1-q.png\" alt=\"points scattered about the line y = -x\" />",
                "options": [
                    {
                        "id": "b21193a20818360ca3df5731a465ba40",
                        "content": "<text hasMath=\"true\">$$u^{(1)} = \\begin{bmatrix}1\\\\0\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "1e018029f18318f7558172a3b868f439",
                        "content": "<text hasMath=\"true\">$$u^{(1)} = \\begin{bmatrix}0\\\\1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "3f5be5c4422c531accf562c15255fc8c",
                        "content": "<text hasMath=\"true\">$$u^{(1)} = \\begin{bmatrix}1/\\sqrt{2}\\\\1/\\sqrt{2}\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "10cdab248750ff85d62b7a3a9f322264",
                        "content": "<text hasMath=\"true\">$$u^{(1)} = \\begin{bmatrix}-1/\\sqrt{2}\\\\1/\\sqrt{2}\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "10cdab248750ff85d62b7a3a9f322264"
                ],
                "explanation": "",
                "videoCuePoint": 520700
            }
        ]
    },
    {
        "videoId": "Iu2Nbr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "00af3273c49ac5e7da4e8d75b436dd50",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In PCA, we obtain $$z\\in\\mathbb{R}^k$$ from $$x\\in\\mathbb{R}^n$$ as follows:</text><text hasMath=\"true\">$$z = \\begin{bmatrix}\\vert &amp; \\vert &amp; &amp; \\vert \\\\ u^{(1)} &amp; u^{(2)} &amp; \\dots &amp; u^{(k)}\\\\ \\vert &amp; \\vert &amp; &amp; \\vert \\end{bmatrix}^T x=\\begin{bmatrix} \\text{---} &amp; (u^{(1)})^T &amp; \\mbox{---}\\\\\\text{---} &amp; (u^{(2)})^T &amp; \\mbox{---}\\\\ &amp; \\vdots &amp; \\\\ \\text{---} &amp; (u^{(k)})^T &amp; \\mbox{---}\\end{bmatrix}x$$</text><text hasMath=\"true\">Which of the following is a correct expression for $$z_j$$?</text>",
                "options": [
                    {
                        "id": "e1f07f18fbd8e40bb61d7a3ededa5139",
                        "content": "<text hasMath=\"true\">$$z_j = (u^{(k)})^T x$$</text>"
                    },
                    {
                        "id": "6c286c983a2213f91862bebd9433983c",
                        "content": "<text hasMath=\"true\">$$z_j = (u^{(j)})^T x_j$$</text>"
                    },
                    {
                        "id": "a54dc81350e7c1ff63605c4c20aa955c",
                        "content": "<text hasMath=\"true\">$$z_j = (u^{(j)})^T x_k$$</text>"
                    },
                    {
                        "id": "05dcf100204f1105ba54f5be0ad48cea",
                        "content": "<text hasMath=\"true\">$$z_j = (u^{(j)})^T x$$</text>"
                    }
                ],
                "answer": [
                    "05dcf100204f1105ba54f5be0ad48cea"
                ],
                "explanation": "",
                "videoCuePoint": 861700
            }
        ]
    },
    {
        "videoId": "Iu530L1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "04b3ddeaa1ecf46d990de6f16b672d1b",
                "type": "checkbox",
                "definition": "<text hasMath=\"true\">Suppose we run PCA with k = n, so that the dimension of the data is not reduced at all. (This is not useful in practice but is a good thought exercise.) Recall that the percent / fraction of variance retained is given by:  $$\\displaystyle\\frac{\\sum_{i=1}^kS_{ii}}{\\sum_{i=1}^nS_{ii}}$$ Which of the following will be true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "7ddf3b6b6201ccb2a4a20984448f8b71",
                        "content": "<text hasMath=\"true\">$$U_\\text{reduce}$$ will be an $$n \\times n$$ matrix.</text>"
                    },
                    {
                        "id": "221d2798434be666edc37eeef25c21c3",
                        "content": "<text hasMath=\"true\">$$x_\\text{approx} = x$$ for every example $$x$$.</text>"
                    },
                    {
                        "id": "0235bd53fe2b6b3e3d33f86b3e616ea5",
                        "content": "<text>The percentage of variance retained will be 100%.</text>"
                    },
                    {
                        "id": "821ba3434c350ab83a20879956e5de95",
                        "content": "<text hasMath=\"true\">We have that $$\\displaystyle\\frac{\\sum_{i=1}^kS_{ii}}{\\sum_{i=1}^nS_{ii}} &gt; 1$$.</text>"
                    }
                ],
                "answer": [
                    "7ddf3b6b6201ccb2a4a20984448f8b71",
                    "221d2798434be666edc37eeef25c21c3",
                    "0235bd53fe2b6b3e3d33f86b3e616ea5"
                ],
                "explanation": "",
                "videoCuePoint": 196500
            }
        ]
    },
    {
        "videoId": "Iu4Cn71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "c293a0716b94aadb55188f4844711372",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Previously, we said that PCA chooses a direction $$u^{(1)}$$ (or k directions $$u^{(1)}, \\dots, u^{(k)}$$) onto which to project the data so as to minimize the (squared) projection error. Another way to say the same is that PCA tries to minimize:</text>",
                "options": [
                    {
                        "id": "6ea48779677d101917b2e7c006c3e0ee",
                        "content": "<text hasMath=\"true\">$$\\frac{1}{m}\\sum_{i=1}^m\\|x^{(i)}\\|^2$$</text>"
                    },
                    {
                        "id": "6f3cfdb81f42baed283cb9293c7d9de0",
                        "content": "<text hasMath=\"true\">$$\\frac{1}{m}\\sum_{i=1}^m\\|x^{(i)}_\\text{approx}\\|^2$$</text>"
                    },
                    {
                        "id": "7299c7e8242158ece0738c856eae7cd1",
                        "content": "<text hasMath=\"true\">$$\\frac{1}{m}\\sum_{i=1}^m\\|x^{(i)}-x^{(i)}_\\text{approx}\\|^2$$</text>"
                    },
                    {
                        "id": "9f7fffacbb3ddcb03ad821d8dff3fde8",
                        "content": "<text hasMath=\"true\">$$\\frac{1}{m}\\sum_{i=1}^m\\|x^{(i)}+x^{(i)}_\\text{approx}\\|^2$$</text>"
                    }
                ],
                "answer": [
                    "7299c7e8242158ece0738c856eae7cd1"
                ],
                "explanation": "",
                "videoCuePoint": 597700
            }
        ]
    },
    {
        "videoId": "Iu9iMb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "66661088cf7c1912eea06741f22234e0",
                "type": "checkbox",
                "definition": "<text>Which of the following are good / recommended applications of PCA? Select all that apply.</text>",
                "options": [
                    {
                        "id": "1d73ca1d10258c0d680f969bf99edbbe",
                        "content": "<text>To compress the data so it takes up less computer memory / disk space</text>"
                    },
                    {
                        "id": "9906a5c863536d1a989fd49dac1389a6",
                        "content": "<text>To reduce the dimension of the input data so as to speed up a learning algorithm</text>"
                    },
                    {
                        "id": "18a473e33d8b61c13a765c565d7b5a80",
                        "content": "<text>Instead of using regularization, use PCA to reduce the number of features to reduce overfitting</text>"
                    },
                    {
                        "id": "ee172d85804faa8f38a696f7677ddc45",
                        "content": "<text>To visualize high-dimensional data (by choosing k = 2 or k = 3)</text>"
                    }
                ],
                "answer": [
                    "1d73ca1d10258c0d680f969bf99edbbe",
                    "9906a5c863536d1a989fd49dac1389a6",
                    "ee172d85804faa8f38a696f7677ddc45"
                ],
                "explanation": "",
                "videoCuePoint": 728600
            }
        ]
    },
    {
        "videoId": "Iu_XYr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "6854fb924b3515e240b052f04b3ba8e5",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Your anomaly detection system flags x as anomalous whenever $$p(x) \\leq \\epsilon$$. Suppose your system is flagging too many things as anomalous that are not actually so (similar to supervised learning, these mistakes are called false positives). What should you do?</text>",
                "options": [
                    {
                        "id": "b8eea6649f88bf072a9320d3f04a5592",
                        "content": "<text hasMath=\"true\">Try increasing $$\\epsilon$$.</text>"
                    },
                    {
                        "id": "607084954f83a24fb787a89357bf5f3d",
                        "content": "<text hasMath=\"true\">Try decreasing $$\\epsilon$$.</text>"
                    }
                ],
                "answer": [
                    "607084954f83a24fb787a89357bf5f3d"
                ],
                "explanation": "",
                "videoCuePoint": 442700
            }
        ]
    },
    {
        "videoId": "IvBzo71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "21fcaa687ab58f0d1456e3b4c7dde560",
                "type": "mcq",
                "definition": "<text>The formula for the Gaussian density is:</text><text hasMath=\"true\">$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\sigma}\\exp\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right)$$</text><text>Which of the following is the formula for the density to the right?</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/16.2-quiz-1-q.png\" alt=\"A gaussian curve centered at -3 with standard deviation 2\" />",
                "options": [
                    {
                        "id": "6d8a40192ca1df49ced869675c23246f",
                        "content": "<text hasMath=\"true\">$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\times2}\\exp\\left(-\\frac{(x-3)^2}{2\\times4}\\right)$$</text>"
                    },
                    {
                        "id": "46db6033cb60d215d4cbc3cb1672e9c0",
                        "content": "<text hasMath=\"true\">$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\times4}\\exp\\left(-\\frac{(x-3)^2}{2\\times2}\\right)$$</text>"
                    },
                    {
                        "id": "236c0373c1e3f2762aa625e0fd185dae",
                        "content": "<text hasMath=\"true\">$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\times2}\\exp\\left(-\\frac{(x+3)^2}{2\\times4}\\right)$$</text>"
                    },
                    {
                        "id": "dfc52b4d617f2ae9988cf78669e13175",
                        "content": "<text hasMath=\"true\">$$p(x) = \\frac{1}{\\sqrt{2\\pi}\\times4}\\exp\\left(-\\frac{(x+3)^2}{2\\times2}\\right)$$</text>"
                    }
                ],
                "answer": [
                    "236c0373c1e3f2762aa625e0fd185dae"
                ],
                "explanation": "",
                "videoCuePoint": 595800
            }
        ]
    },
    {
        "videoId": "IvDo1L1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "ee46e63899c9907db7e61b3b287c3b9d",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Given a training set $$\\{x^{(1)}, \\dots, x^{(m)}\\}$$, how would you estimate each $$\\mu_j$$ and $$\\sigma_j^2$$ (Note $$\\mu_j\\in\\mathbb{R},\\sigma_j^2\\in\\mathbb{R}$$.)</text>",
                "options": [
                    {
                        "id": "ad825030a14eed5c432b2a7781afaa78",
                        "content": "<text hasMath=\"true\">$$\\displaystyle \\mu_j = \\frac{1}{m}\\sum_{i=1}^m x^{(i)},\\ \\sigma_j^2 = \\frac{1}{m}\\sum_{i=1}^m(x^{(i)} - \\mu)^2$$</text>"
                    },
                    {
                        "id": "da60bbe9df770e38134181686fd55ba9",
                        "content": "<text hasMath=\"true\">$$\\displaystyle \\mu_j = \\frac{1}{m}\\sum_{i=1}^m (x_j^{(i)})^2,\\ \\sigma_j^2 = \\frac{1}{m}\\sum_{i=1}^m(x_j^{(i)} - \\mu_j)^2$$</text>"
                    },
                    {
                        "id": "a92ab4def0acdeb060cddc9c6aecbde8",
                        "content": "<text hasMath=\"true\">$$\\displaystyle \\mu_j = \\frac{1}{m}\\sum_{i=1}^m x_j^{(i)},\\ \\sigma_j^2 = \\frac{1}{m}\\sum_{i=1}^m(x^{(i)} - \\mu)^2$$</text>"
                    },
                    {
                        "id": "847d1ad96ce6d6c74d7763aa9b479634",
                        "content": "<text hasMath=\"true\">$$\\displaystyle \\mu_j = \\frac{1}{m}\\sum_{i=1}^m x_j^{(i)},\\ \\sigma_j^2 = \\frac{1}{m}\\sum_{i=1}^m(x_j^{(i)} - \\mu_j)^2$$</text>"
                    }
                ],
                "answer": [
                    "847d1ad96ce6d6c74d7763aa9b479634"
                ],
                "explanation": "",
                "videoCuePoint": 273500
            }
        ]
    },
    {
        "videoId": "IvFeBb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5a9cc0e33d8bda7720bb611de21b8f7d",
                "type": "mcq",
                "definition": "<text>Suppose you have fit a model p(x). When evaluating on the cross validation set or test set, your algorithm predicts:</text><text hasMath=\"true\">$$y = \\left\\{\\begin{array}{ll} 1 &amp; \\mbox{if } p(x) \\leq \\epsilon\\\\ 0 &amp; \\mbox{if } p(x) &gt; \\epsilon\\end{array}\\right.$$</text><text>Is classification accuracy a good way to measure the algorithm's performance?</text>",
                "options": [
                    {
                        "id": "7cd42cc20b2490618c20bcf13fb9e15e",
                        "content": "<text>Yes, because we have labels in the cross validation / test sets.</text>"
                    },
                    {
                        "id": "8b4bf122e417bdaaeb7fcc0b4f86a03b",
                        "content": "<text>No, because we do not have labels in the cross validation / test sets.</text>"
                    },
                    {
                        "id": "92fab5a2197f103bd7091f971bacf02e",
                        "content": "<text>No, because of skewed classes (so an algorithm that always predicts y = 0 will have high accuracy).</text>"
                    },
                    {
                        "id": "bb3ef19df28b80a11d75766cc868b85f",
                        "content": "<text>No for the cross validation set; yes for the test set.</text>"
                    }
                ],
                "answer": [
                    "92fab5a2197f103bd7091f971bacf02e"
                ],
                "explanation": "",
                "videoCuePoint": 611600
            }
        ]
    },
    {
        "videoId": "IvGsJr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "b90b86698c1a9a3608141cae08a76fd5",
                "type": "checkbox",
                "definition": "<text>Which of the following problems would you approach with an anomaly detection algorithm (rather than a supervised learning algorithm)? Check all that apply.</text>",
                "options": [
                    {
                        "id": "9bba4c6e801713a1fb28246fdac93346",
                        "content": "<text>You run a power utility (supplying electricity to customers) and want to monitor your electric plants to see if any one of them might be behaving strangely.</text>"
                    },
                    {
                        "id": "92169598647c8d07387e93f5df77b231",
                        "content": "<text>You run a power utility and want to predict tomorrow\u2019s expected demand for electricity (so that you can plan to ramp up an appropriate amount of generation capacity).</text>"
                    },
                    {
                        "id": "fec9589722c23baee8cb926200a79b21",
                        "content": "<text>A computer vision / security application, where you examine video images to see if anyone in your company\u2019s parking lot is acting in an unusual way.</text>"
                    },
                    {
                        "id": "fe5a322095d8da44092b6b1354dd8265",
                        "content": "<text>A computer vision application, where you examine an image of a person entering your retail store to determine if the person is male or female.</text>"
                    }
                ],
                "answer": [
                    "9bba4c6e801713a1fb28246fdac93346",
                    "fec9589722c23baee8cb926200a79b21"
                ],
                "explanation": "",
                "videoCuePoint": 422400
            }
        ]
    },
    {
        "videoId": "IvH6R71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "5e31ccc98b0d4747929b08552099c32e",
                "type": "mcq",
                "definition": "<text>Suppose your anomaly detection algorithm is performing poorly and outputs a large value of p(x) for many normal examples and for many anomalous examples in your cross validation dataset. Which of the following changes to your algorithm is most likely to help?</text>",
                "options": [
                    {
                        "id": "621f1b0d024829cb1062a2ddf3b7c0d8",
                        "content": "<text>Try using fewer features.</text>"
                    },
                    {
                        "id": "c99263341789402d741e4568dc9fd05a",
                        "content": "<text>Try coming up with more features to distinguish between the normal and the anomalous examples.</text>"
                    },
                    {
                        "id": "370bdad353cb0b6ef2c2a7c79b4fca65",
                        "content": "<text>Get a larger training set (of normal examples) with which to fit p(x).</text>"
                    },
                    {
                        "id": "b63014f98e78955bcfd2e8a397c53e16",
                        "content": "<text hasMath=\"true\">Try changing $$\\epsilon$$.</text>"
                    }
                ],
                "answer": [
                    "c99263341789402d741e4568dc9fd05a"
                ],
                "explanation": "",
                "videoCuePoint": 710600
            }
        ]
    },
    {
        "videoId": "IvK9mL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "d9e6137fa4a4e5818e82a7ac067427e8",
                "type": "mcq",
                "definition": "<text>Consider the following multivariate Gaussian:</text><img src=\"http://spark-public.s3.amazonaws.com/ml/images/16.7-quiz-1-q.png\" alt=\"Bivariate Gaussian density, centered at (1,0). Both variables have unit variance and are inversely correlated.\" /><text hasMath=\"true\">Which of the following are the $$\\mu$$ and $$\\Sigma$$ for this distribution?</text>",
                "options": [
                    {
                        "id": "fbe9fc7f307f2fcffa1e70ea68c3873f",
                        "content": "<text hasMath=\"true\">$$\\mu=\\begin{bmatrix}1\\\\0\\end{bmatrix},\\ \\Sigma=\\begin{bmatrix}1 &amp; 0.3 \\\\ 0.3 &amp; 1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "134062052e36f71146f57c86dacfcff2",
                        "content": "<text hasMath=\"true\">$$\\mu=\\begin{bmatrix}0\\\\1\\end{bmatrix},\\ \\Sigma=\\begin{bmatrix}1 &amp; 0.3 \\\\ 0.3 &amp; 1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "7fd268c3e2ebbcd563987c892960c010",
                        "content": "<text hasMath=\"true\">$$\\mu=\\begin{bmatrix}1\\\\0\\end{bmatrix},\\ \\Sigma=\\begin{bmatrix}1 &amp; -0.3 \\\\ -0.3 &amp; 1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "d1d51de061005bfe857471cc10a5c9df",
                        "content": "<text hasMath=\"true\">$$\\mu=\\begin{bmatrix}0\\\\1\\end{bmatrix},\\ \\Sigma=\\begin{bmatrix}1 &amp; -0.3 \\\\ -0.3 &amp; 1\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "7fd268c3e2ebbcd563987c892960c010"
                ],
                "explanation": "",
                "videoCuePoint": 799700
            }
        ]
    },
    {
        "videoId": "IvMyyb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "270b0a74e84141643ddd2137c7c47a1d",
                "type": "checkbox",
                "definition": "<text hasMath=\"true\">Consider applying anomaly detection using a training set $$\\{x^{(1)}, \\dots, x^{(m)}\\}$$ where $$x^{(i)}\\in\\mathbb{R}^n$$. Which of the following statements are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "f1892ef6c34fa2d106aec84d77a9547d",
                        "content": "<text hasMath=\"true\">The original model $$p(x_1;\\mu_1,\\sigma_1^2)\\times\\dots\\times p(x_n;\\mu_n,\\sigma_n^2)$$ corresponds to a multivariate Gaussian where the contours of $$p(x;\\mu,\\Sigma)$$ are axis-aligned.</text>"
                    },
                    {
                        "id": "910301431cd467e9c770ae520e5d8d14",
                        "content": "<text>Using the multivariate Gaussian model is advantageous when m (the training set size) is very small (m &lt; n).</text>"
                    },
                    {
                        "id": "a16ce71371544a9c7f6ca46edb3277a7",
                        "content": "<text>The multivariate Gaussian model can automatically capture correlations between different features in x.</text>"
                    },
                    {
                        "id": "3bc045d048417adfbb72bc2e9c79b6dd",
                        "content": "<text>The original model can be more computationally efficient than the multivariate Gaussian model, and thus might scale better to very large values of n (number of features).</text>"
                    }
                ],
                "answer": [
                    "f1892ef6c34fa2d106aec84d77a9547d",
                    "a16ce71371544a9c7f6ca46edb3277a7",
                    "3bc045d048417adfbb72bc2e9c79b6dd"
                ],
                "explanation": "",
                "videoCuePoint": 823700
            }
        ]
    },
    {
        "videoId": "IvPPCr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "k6tAxrLrEeSTXyIACzQGuw@2",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In our notation, $$r(i,j)=1$$ if user $$j$$ has rated movie $$i$$, and $$y^{(i,j)}$$ is his rating on that movie. Consider the following example (no. of movies $$n_m=2$$, no. of users $$n_u=3$$):</text><table rows=\"3\" columns=\"4\"><tr><td><text>. </text></td><td><text>User 1</text></td><td><text>User 2</text></td><td><text>User 3</text></td></tr><tr><td><text>Movie 1</text></td><td><text>0</text></td><td><text>1</text></td><td><text>?</text></td></tr><tr><td><text>Movie 2</text></td><td><text>?</text></td><td><text>5</text></td><td><text>5</text></td></tr></table><text hasMath=\"true\"> What is $$r(2,1)$$? How about $$y^{(2,1)}$$?</text>",
                "options": [
                    {
                        "id": "01ef40a66829562083c8000be90f1855",
                        "content": "<text hasMath=\"true\">$$r(2,1) = 0,\\ y^{(2,1)} = 1$$</text>"
                    },
                    {
                        "id": "273fb02a887209c1a44254902e02c861",
                        "content": "<text hasMath=\"true\">$$r(2,1) = 1,\\ y^{(2,1)} = 1$$</text>"
                    },
                    {
                        "id": "aea729d00683c2d3df400d72e8098f5c",
                        "content": "<text hasMath=\"true\">$$r(2,1) = 0,\\ y^{(2,1)} = \\text{undefined}$$</text>"
                    },
                    {
                        "id": "75b5475c3ab032332f98011d1ed34199",
                        "content": "<text hasMath=\"true\">$$r(2,1) = 1,\\ y^{(2,1)} = \\text{undefined}$$</text>"
                    }
                ],
                "answer": [
                    "aea729d00683c2d3df400d72e8098f5c"
                ],
                "explanation": "",
                "videoCuePoint": 464700
            }
        ]
    },
    {
        "videoId": "IvREO71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "36479f5e7e72617ec5ec73bb6b65b24c",
                "type": "mcq",
                "definition": "<text>Consider the following set of movie ratings:</text><table rows=\"6\" columns=\"7\"><tr><td><text>Movie</text></td><td><text>Alice (1)</text></td><td><text>Bob (2)</text></td><td><text>Carol (3)</text></td><td><text>David (4)</text></td><td><text>(romance)</text></td><td><text>(action)</text></td></tr><tr><td><text>Love at last</text></td><td><text>5</text></td><td><text>5</text></td><td><text>0</text></td><td><text>0</text></td><td><text>0.9</text></td><td><text>0</text></td></tr><tr><td><text>Romance forever</text></td><td><text>5</text></td><td><text>?</text></td><td><text>?</text></td><td><text>0</text></td><td><text>1.0</text></td><td><text>0.01</text></td></tr><tr><td><text>Cute puppies of love</text></td><td><text>?</text></td><td><text>4</text></td><td><text>0</text></td><td><text>?</text></td><td><text>0.99</text></td><td><text>0</text></td></tr><tr><td><text>Nonstop car chases</text></td><td><text>0</text></td><td><text>0</text></td><td><text>5</text></td><td><text>4</text></td><td><text>0.1</text></td><td><text>1.0</text></td></tr><tr><td><text>Swords vs. karate</text></td><td><text>0</text></td><td><text>0</text></td><td><text>5</text></td><td><text>?</text></td><td><text>0</text></td><td><text>0.9</text></td></tr></table><text hasMath=\"true\">Which of the following is a reasonable value for $$\\theta^{(3)}$$? Recall that $$x_0 = 1$$.</text>",
                "options": [
                    {
                        "id": "67e5ff4ee5bff5cb2cbfbe05c75fee29",
                        "content": "<text hasMath=\"true\">$$\\theta^{(3)} = \\begin{bmatrix}0\\\\5\\\\0\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "ecb5f31b6a12b9601de757af08d310e2",
                        "content": "<text hasMath=\"true\">$$\\theta^{(3)} = \\begin{bmatrix}0\\\\0\\\\1\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "cfe04fc4659b03dac634d94229364b4b",
                        "content": "<text hasMath=\"true\">$$\\theta^{(3)} = \\begin{bmatrix}1\\\\0\\\\4\\end{bmatrix}$$</text>"
                    },
                    {
                        "id": "d9d810c541586f05aafb736b3fe680ce",
                        "content": "<text hasMath=\"true\">$$\\theta^{(3)} = \\begin{bmatrix}0\\\\0\\\\5\\end{bmatrix}$$</text>"
                    }
                ],
                "answer": [
                    "d9d810c541586f05aafb736b3fe680ce"
                ],
                "explanation": "",
                "videoCuePoint": 373600
            }
        ]
    },
    {
        "videoId": "IvSSXL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "c3852a52e0a8e44b8633811a4b5aefef",
                "type": "mcq",
                "definition": "<text>Consider the following movie ratings:</text><table rows=\"2\" columns=\"5\"><tr><td><text>.</text></td><td><text>User 1</text></td><td><text>User 2</text></td><td><text>User 3</text></td><td><text>(romance)</text></td></tr><tr><td><text>Movie 1</text></td><td><text>0</text></td><td><text>1.5</text></td><td><text>2.5</text></td><td><text>?</text></td></tr></table><text hasMath=\"true\">Note that there is only one feature $$x_1$$. Suppose that:</text><text hasMath=\"true\"> $$\\theta^{(1)} = \\begin{bmatrix}0\\\\0\\end{bmatrix},\\ \\theta^{(2)} = \\begin{bmatrix}0\\\\3\\end{bmatrix},\\ \\theta^{(3)} = \\begin{bmatrix}0\\\\5\\end{bmatrix}$$</text><text hasMath=\"true\">What would be a reasonable value for $$x_1^{(1)}$$ (the value denoted \"?\" in the table above)?</text>",
                "options": [
                    {
                        "id": "fb63c4b691978e6f5aeb6a72cdcfac03",
                        "content": "<text>0.5</text>"
                    },
                    {
                        "id": "41691843feabb50d4cca3c60e99e5134",
                        "content": "<text>1</text>"
                    },
                    {
                        "id": "b9f039015bf75cf083bf7cbee5c9ed91",
                        "content": "<text>2</text>"
                    },
                    {
                        "id": "8d9cfb37b38e1d921e8d4327aa0a2aa7",
                        "content": "<text>Any of these values would be equally reasonable.</text>"
                    }
                ],
                "answer": [
                    "fb63c4b691978e6f5aeb6a72cdcfac03"
                ],
                "explanation": "",
                "videoCuePoint": 276800
            },
            {
                "id": "c9edaa1b01fc2ef39bc32dc0b82fc849",
                "type": "mcq",
                "definition": "<text>Suppose you use gradient descent to minimize:</text><text hasMath=\"true\">$$\\displaystyle \\min_{x^{(1)},\\dots,x^{(n_m)}} \\frac{1}{2}\\sum_{i=1}^{n_m}\\sum_{j:r(i,j)=1}\\left((\\theta^{(j)})^T x^{(i)}-y^{(i,j)}\\right)^2 + \\frac{\\lambda}{2}\\sum_{i=1}^{n_m}\\sum_{k=1}^n(x_k^{(i)})^2$$</text><text hasMath=\"true\">Which of the following is a correct gradient descent update rule for $$i\\neq 0$$?</text>",
                "options": [
                    {
                        "id": "b12191c7a2af9939525ca15bfbcbc720",
                        "content": "<text hasMath=\"true\">$$x_k^{(i)} := x_k^{(i)} + \\alpha\\left(\\sum_{j:r(i,j)=1}\\left((\\theta^{(j)})^T(x^{(i)}) - y^{(i,j)}\\right)\\theta_k^{(j)}\\right)$$</text>"
                    },
                    {
                        "id": "3b75310e01ce742112e27ae97f22485f",
                        "content": "<text hasMath=\"true\">$$x_k^{(i)} := x_k^{(i)} - \\alpha\\left(\\sum_{j:r(i,j)=1}\\left((\\theta^{(j)})^T(x^{(i)}) - y^{(i,j)}\\right)\\theta_k^{(j)}\\right)$$</text>"
                    },
                    {
                        "id": "6ac841f8720895de3048b7b45a5d0336",
                        "content": "<text hasMath=\"true\">$$x_k^{(i)} := x_k^{(i)} + \\alpha\\left(\\sum_{j:r(i,j)=1}\\left((\\theta^{(j)})^T(x^{(i)}) - y^{(i,j)}\\right)\\theta_k^{(j)} + \\lambda x_k^{(i)}\\right)$$</text>"
                    },
                    {
                        "id": "d8cf4169e374206811454000a3c4301e",
                        "content": "<text hasMath=\"true\">$$x_k^{(i)} := x_k^{(i)} - \\alpha\\left(\\sum_{j:r(i,j)=1}\\left((\\theta^{(j)})^T(x^{(i)}) - y^{(i,j)}\\right)\\theta_k^{(j)}+ \\lambda x_k^{(i)}\\right)$$</text>"
                    }
                ],
                "answer": [
                    "d8cf4169e374206811454000a3c4301e"
                ],
                "explanation": "",
                "videoCuePoint": 427800
            }
        ]
    },
    {
        "videoId": "IvTgfb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "cc768bf5b7dceb35d7c5fb6aaef8cfb3",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">In the algorithm we described, we initialized $$x^{(1)}, \\dots, x^{(n_m)}$$ and $$\\theta^{(1)},\\dots,\\theta^{(n_u)}$$ to small random values. Why is this?</text>",
                "options": [
                    {
                        "id": "18786e7d273c00d4c12c46ee51f8ad50",
                        "content": "<text>This step is optional. Initializing to all 0\u2019s would work just as well.</text>"
                    },
                    {
                        "id": "5fb1eefc42e6b38dad6f4786c38dcafb",
                        "content": "<text>Random initialization is always necessary when using gradient descent on any problem.</text>"
                    },
                    {
                        "id": "7cae376be1a8a3e76bb8d7a9fd5a3916",
                        "content": "<text hasMath=\"true\">This ensures that $$x^{(i)} \\neq \\theta^{(j)}$$ for any $$i,j$$.</text>"
                    },
                    {
                        "id": "35143edfd6421a9e0f7dfd93672294dd",
                        "content": "<text hasMath=\"true\">This serves as symmetry breaking (similar to the random initialization of a neural network\u2019s parameters) and ensures the algorithm learns features $$x^{(1)}, \\dots, x^{(n_m)}$$ that are different from each other.</text>"
                    }
                ],
                "answer": [
                    "35143edfd6421a9e0f7dfd93672294dd"
                ],
                "explanation": "",
                "videoCuePoint": 486300
            }
        ]
    },
    {
        "videoId": "IvZADr1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "a32d3489f3a2b4a2300a6da656f5257b",
                "type": "mcq",
                "definition": "<text hasMath=\"true\">Let $$X = \\begin{bmatrix} - &amp; (x^{(1)})^T &amp; - \\\\ &amp; \\vdots &amp; \\\\ - &amp; (x^{(n_m)} &amp; - \\end{bmatrix},\\ \\Theta = \\begin{bmatrix} - &amp; (\\theta^{(1)})^T &amp; - \\\\ &amp; \\vdots &amp; \\\\ - &amp; (\\theta^{(n_u)} &amp; - \\end{bmatrix}$$.</text><text>What is another way of writing the following:</text><text hasMath=\"true\">$$\\displaystyle \\begin{bmatrix} (x^{(1)})^T(\\theta^{(1)}) &amp; \\ldots &amp; (x^{(1)})^T(\\theta^{(n_u)})\\\\ \\vdots &amp; \\ddots &amp; \\vdots \\\\ (x^{(n_m)})^T(\\theta^{(1)}) &amp; \\ldots &amp; (x^{(n_m)})^T(\\theta^{(n_u)})\\end{bmatrix}$$</text>",
                "options": [
                    {
                        "id": "e2c34a2b1f86c8ffb22141576685a567",
                        "content": "<text hasMath=\"true\">$$X\\Theta$$</text>"
                    },
                    {
                        "id": "b53a1c72818f14efec26788dbaefbd14",
                        "content": "<text hasMath=\"true\">$$X^T\\Theta$$</text>"
                    },
                    {
                        "id": "28ea2bd1ee685bd59ad00cabc128ec9f",
                        "content": "<text hasMath=\"true\">$$X\\Theta^T$$</text>"
                    },
                    {
                        "id": "6d6c0a054d48785735a26e349cbf5e37",
                        "content": "<text hasMath=\"true\">$$\\Theta^TX^T$$</text>"
                    }
                ],
                "answer": [
                    "28ea2bd1ee685bd59ad00cabc128ec9f"
                ],
                "explanation": "",
                "videoCuePoint": 311700
            }
        ]
    },
    {
        "videoId": "Iva1P71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "cea8fad2299fa9f620628fca53b37d31",
                "type": "mcq",
                "definition": "<text>We talked about mean normalization. However, unlike some other applications of feature scaling, we did not scale the movie ratings by dividing by the range (max \u2013 min value). This is because:</text>",
                "options": [
                    {
                        "id": "95fe93bfc29772ece0fd65bde026956c",
                        "content": "<text>This sort of scaling is not useful when the value being predicted is real-valued.</text>"
                    },
                    {
                        "id": "f65714f0f64fcc5e70ac3f86560b3b08",
                        "content": "<text>All the movie ratings are already comparable (e.g., 0 to 5 stars), so they are already on similar scales.</text>"
                    },
                    {
                        "id": "4ce9c35d25f7358bc30aee079ea776ac",
                        "content": "<text>Subtracting the mean is mathematically equivalent to dividing by the range.</text>"
                    },
                    {
                        "id": "065a0b2e4505a4f784c6c72004fb2768",
                        "content": "<text>This makes the overall algorithm significantly more computationally efficient.</text>"
                    }
                ],
                "answer": [
                    "f65714f0f64fcc5e70ac3f86560b3b08"
                ],
                "explanation": "",
                "videoCuePoint": 498500
            }
        ]
    },
    {
        "videoId": "IvcqcL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "bc2ab645ba757cd97d3f50e3993d3f64",
                "type": "mcq",
                "definition": "<text>Suppose you are facing a supervised learning problem and have a very large dataset (m = 100,000,000). How can you tell if using all of the data is likely to perform much better than using a small subset of the data (say m = 1,000)?</text>",
                "options": [
                    {
                        "id": "699dc3302a3e10b5e2de0d0fbb6a5bf3",
                        "content": "<text>There is no need to verify this; using a larger dataset always gives much better performance.</text>"
                    },
                    {
                        "id": "dec397d6bde7a7e738829921194d2675",
                        "content": "<text hasMath=\"true\">Plot $$J_\\text{train}(\\theta)$$ as a function of the number of iterations of the optimization algorithm (such as gradient descent).</text>"
                    },
                    {
                        "id": "ecb2746a6626b5430f3c5ffe3e2cd7f0",
                        "content": "<text hasMath=\"true\">Plot a learning curve ($$J_\\text{train}(\\theta)$$ and $$J_\\text{CV}(\\theta)$$, plotted as a function of m) for some range of values of m (say up to m = 1,000) and verify that the algorithm has bias when m is small.</text>"
                    },
                    {
                        "id": "b7aaf2b668ebde8573b84c1fd029613b",
                        "content": "<text>Plot a learning curve for a range of values of m and verify that the algorithm has high variance when m is small.</text>"
                    }
                ],
                "answer": [
                    "b7aaf2b668ebde8573b84c1fd029613b"
                ],
                "explanation": "",
                "videoCuePoint": 204500
            }
        ]
    },
    {
        "videoId": "Ivd4kb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "f6ab17cb348527a33e403de57224e3f3",
                "type": "checkbox",
                "definition": "<text>Which of the following statements about stochastic gradient descent are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "fbe191938968da0c127bed62b9bbc84c",
                        "content": "<text>When the training set size m is very large, stochastic gradient descent can be much faster than gradient descent.</text>"
                    },
                    {
                        "id": "9b3708e841f3ba3762c8d2b2c9ff41ec",
                        "content": "<text hasMath=\"true\">The cost function $$J_\\text{train}(\\theta) = \\frac{1}{2m}\\sum_{i=1}^m (h_\\theta(x^{(i)}) - y^{(i)})^2$$ should go down with every iteration of batch gradient descent (assuming a well-tuned learning rate $$\\alpha$$) but not necessarily with stochastic gradient descent.</text>"
                    },
                    {
                        "id": "1f997e560b136e2cabdf8d4b1881db33",
                        "content": "<text>Stochastic gradient descent is applicable only to linear regression but not to other models (such as logistic regression or neural networks).</text>"
                    },
                    {
                        "id": "f214c40c4956683ff9a580807e9e6901",
                        "content": "<text>Before beginning the main loop of stochastic gradient descent, it is a good idea to \"shuffle\" your training data into a random order.</text>"
                    }
                ],
                "answer": [
                    "fbe191938968da0c127bed62b9bbc84c",
                    "9b3708e841f3ba3762c8d2b2c9ff41ec",
                    "f214c40c4956683ff9a580807e9e6901"
                ],
                "explanation": "",
                "videoCuePoint": 787500
            }
        ]
    },
    {
        "videoId": "IvgU0r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "db7ac39b702390eb0929ce1ceb07b189",
                "type": "mcq",
                "definition": "<text>Suppose you use mini-batch gradient descent on a training set of size m, and you use a mini-batch size of b. The algorithm becomes the same as batch gradient descent if:</text>",
                "options": [
                    {
                        "id": "9c69c383e70e17dcde13a8adaf22698f",
                        "content": "<text>b = 1</text>"
                    },
                    {
                        "id": "066de6f1241f017dbaa5475d83d53ad0",
                        "content": "<text>b = m / 2</text>"
                    },
                    {
                        "id": "2cf8876ae1c15a32cee66eccdd0a1958",
                        "content": "<text>b = m</text>"
                    },
                    {
                        "id": "6105b586293c6cdcb44177510662bf43",
                        "content": "<text>None of the above</text>"
                    }
                ],
                "answer": [
                    "2cf8876ae1c15a32cee66eccdd0a1958"
                ],
                "explanation": "",
                "videoCuePoint": 346800
            }
        ]
    },
    {
        "videoId": "IvlNU71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "72b00ee9ed4d3116d52a59231660e6f2",
                "type": "checkbox",
                "definition": "<text>Which of the following statements about stochastic gradient descent are true? Check all that apply.</text>",
                "options": [
                    {
                        "id": "ad53f5bb91a1d552ccf4ead01b5eb62a",
                        "content": "<text>Picking a learning rate \u03b1 that is very small has no disadvantage and can only speed up learning.</text>"
                    },
                    {
                        "id": "a1cbca93567995e8a136888d72100db9",
                        "content": "<text hasMath=\"true\">If we reduce the learning rate $$\\alpha$$ (and run stochastic gradient descent long enough), it\u2019s possible that we may find a set of better parameters than with larger $$\\alpha$$.</text>"
                    },
                    {
                        "id": "43dc54574393b39177ba47d98ee9c764",
                        "content": "<text hasMath=\"true\">If we want stochastic gradient descent to converge to a (local) minimum rather than wander of \"oscillate\" around it, we should slowly increase $$\\alpha$$ over time.</text>"
                    },
                    {
                        "id": "8dd37a4bb12819f6c06cfef58d77a350",
                        "content": "<text hasMath=\"true\">If we plot $$\\text{cost}(\\theta, (x^{(i)}, y^{(i)}))$$ (averaged over the last 1000 examples) and stochastic gradient descent does not seem to be reducing the cost, one possible problem may be that the learning rate $$\\alpha$$ is poorly tuned.</text>"
                    }
                ],
                "answer": [
                    "a1cbca93567995e8a136888d72100db9",
                    "8dd37a4bb12819f6c06cfef58d77a350"
                ],
                "explanation": "",
                "videoCuePoint": 658600
            }
        ]
    },
    {
        "videoId": "IvnChL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "85d40f56b8198ce36032e931b35d292a",
                "type": "checkbox",
                "definition": "<text>Some of the advantages of using an online learning algorithm are:</text>",
                "options": [
                    {
                        "id": "00fd785e43c3b47f97317fbd947dcc9d",
                        "content": "<text hasMath=\"true\">It can adapt to changing user tastes (i.e., if $$p(y\\vert x;\\theta)$$ changes over time).</text>"
                    },
                    {
                        "id": "a4ed8b6150ed24ec857cd6c65e90b0ff",
                        "content": "<text hasMath=\"true\">There is no need to pick a learning rate $$\\alpha$$.</text>"
                    },
                    {
                        "id": "22f54e32976510e7cbbca6fb2ebc187a",
                        "content": "<text>It allows us to learn from a continuous stream of data, since we use each example once then no longer need to process it again.</text>"
                    },
                    {
                        "id": "b2fc1771d769a19a5ae327d02718261e",
                        "content": "<text>It does not require that good features be chosen for the learning task.</text>"
                    }
                ],
                "answer": [
                    "00fd785e43c3b47f97317fbd947dcc9d",
                    "22f54e32976510e7cbbca6fb2ebc187a"
                ],
                "explanation": "",
                "videoCuePoint": 724600
            }
        ]
    },
    {
        "videoId": "Ivo3tb1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "0d200af3da37cab2aa3e859d15c54c8f",
                "type": "mcq",
                "definition": "<text>Suppose you apply the map-reduce method to train a neural network on ten machines. In each iteration, what will each of the machines do?</text>",
                "options": [
                    {
                        "id": "408c24b1e5c2d6d8d53e2d91315da40c",
                        "content": "<text>Compute either forward propagation or back propagation on 1/5 of the data.</text>"
                    },
                    {
                        "id": "34eda049d4b2b0947d24adcee12ae539",
                        "content": "<text>Compute forward propagation and back propagation on 1/10 of the data to compute the derivative with respect to that 1/10 of the data.</text>"
                    },
                    {
                        "id": "5e79c260603e2add08c8c33737ae6859",
                        "content": "<text>Compute only forward propagation on 1/10 of the data. (The centralized machine then performs back propagation on all the data).</text>"
                    },
                    {
                        "id": "acdb2f6eca90ffd16bce4ad0e414a6f2",
                        "content": "<text>Compute back propagation on 1/10 of the data (after the centralized machine has computed forward propagation on all of the data).</text>"
                    }
                ],
                "answer": [
                    "34eda049d4b2b0947d24adcee12ae539"
                ],
                "explanation": "",
                "videoCuePoint": 809600
            }
        ]
    },
    {
        "videoId": "Ivqs5r1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "315c02d43f693b1d1c416550e5ee1579",
                "type": "mcq",
                "definition": "<text>When someone refers to a \u201cmachine learning pipeline,\u201d he or she is referring to:</text>",
                "options": [
                    {
                        "id": "6e7caf71533d01c1a20813e1a93463c7",
                        "content": "<text>A PhotoOCR system.</text>"
                    },
                    {
                        "id": "fcde446bdf4b243243fd556234cb7708",
                        "content": "<text>A character recognition system.</text>"
                    },
                    {
                        "id": "79b73dc245d14399a382ab8cbf51bc2c",
                        "content": "<text>A system with many stages / components, several of which may use machine learning.</text>"
                    },
                    {
                        "id": "977d7b7e12b66666e9db323ca173607f",
                        "content": "<text>An application in plumbing. (Haha.)</text>"
                    }
                ],
                "answer": [
                    "79b73dc245d14399a382ab8cbf51bc2c"
                ],
                "explanation": "",
                "videoCuePoint": 397600
            }
        ]
    },
    {
        "videoId": "IvsiF71-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "e31bc125f0a632612b74d21176e67783",
                "type": "mcq",
                "definition": "<text>Suppose you are running a text detector using 20x20 image patches. You run the classifier on a 200x200 image and when using sliding window, you \u201cstep\u201d the detector by 4 pixels each time. (For this problem assume you apply the algorithm at only one scale.) About how many times will you end up running your classifier on a single image? (Pick the closest answer.)</text>",
                "options": [
                    {
                        "id": "625aa10684422a13a98987e8d5a3ac52",
                        "content": "<text>About 100 times.</text>"
                    },
                    {
                        "id": "4d1b87a75baee809dedd96a4af2e50f3",
                        "content": "<text>About 400 times. </text>"
                    },
                    {
                        "id": "199190233f0020b5db8f64b47b9773ab",
                        "content": "<text>About 2,500 times.</text>"
                    },
                    {
                        "id": "707c5bc80895cc65b0c8a313bae5ac90",
                        "content": "<text>About 40,000 times.</text>"
                    }
                ],
                "answer": [
                    "199190233f0020b5db8f64b47b9773ab"
                ],
                "explanation": "",
                "videoCuePoint": 644500
            }
        ]
    },
    {
        "videoId": "IvtwOL1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "6154392209e9092a4f26f58bdca96b21",
                "type": "mcq",
                "definition": "<text>You\u2019ve just joined a product group that has been developing a machine learning application for the last 12 months using 1,000 training examples. Suppose that by manually collecting and labeling examples, it takes you an average of 10 seconds to obtain one extra training example. Suppose you work 8 hours a day. How many days will it take you to get 10,000 examples? (Pick the closest answer.)</text>",
                "options": [
                    {
                        "id": "6ab5c578cea1590d387885d4d4089c05",
                        "content": "<text>About 1 day.</text>"
                    },
                    {
                        "id": "4b77e269c7520b82196d1cae9d4aa081",
                        "content": "<text>About 3.5 days. </text>"
                    },
                    {
                        "id": "812c68de327e916d54a86b77bedf17e0",
                        "content": "<text>About 28 days.</text>"
                    },
                    {
                        "id": "49179d2ad993ea0a73b00987cda5d89a",
                        "content": "<text>About 200 days.</text>"
                    }
                ],
                "answer": [
                    "4b77e269c7520b82196d1cae9d4aa081"
                ],
                "explanation": "",
                "videoCuePoint": 925700
            },
            {
                "id": "7a0b6840fe7e95897c280c307aa20ee1",
                "type": "mcq",
                "definition": "<text>Suppose you are training a linear regression model with m examples by minimizing:</text><text hasMath=\"true\">$$J(\\theta) = \\frac{1}{2m}\\sum_{i=1}^m(h_\\theta(x^{(i)}) - y^{(i)})^2)$$</text><text hasMath=\"true\">Suppose you duplicate every example by making two identical copies of it. That is, where you previously had one example $$(x^{(i)}, y^{(i)})$$, you now have two copies of it, so you now have 2m examples. Is this likely to help?</text>",
                "options": [
                    {
                        "id": "4ffdbe64275dd6d48b7c09cca0c247a7",
                        "content": "<text>Yes, because increasing the training set size will reduce variance.</text>"
                    },
                    {
                        "id": "b562db6ed73b8892497f72251808e673",
                        "content": "<text>Yes, so long as you are using a large number of features (a \u201clow bias\u201d learning algorithm).</text>"
                    },
                    {
                        "id": "d0f9bfb6483b0f315b7cca4026b0cd4d",
                        "content": "<text>No. You may end up with different parameters \u03b8, but they are unlikely to do any better than the ones learned from the original training set.</text>"
                    },
                    {
                        "id": "9da582dbf294547873e19cbff2484a10",
                        "content": "<text>No, and in fact you will end up with the same parameters \u03b8 as before you duplicated the data.</text>"
                    }
                ],
                "answer": [
                    "9da582dbf294547873e19cbff2484a10"
                ],
                "explanation": "",
                "videoCuePoint": 557600
            }
        ]
    },
    {
        "videoId": "Ivvlab1-EeSqHiIAC2idzw",
        "questions": [
            {
                "id": "af72af8f5145bfb29cd414d1e54cb1d4",
                "type": "checkbox",
                "definition": "<text>Suppose you perform ceiling analysis on a pipelined machine learning system, and when we plug in the ground-truth labels for one of the components, the performance of the overall system improves very little. This probably means: (check all that apply)</text>",
                "options": [
                    {
                        "id": "feb3a2a43cbc7a093ef7f3180a1ca630",
                        "content": "<text>We should dedicate significant effort to collecting more data for that component.</text>"
                    },
                    {
                        "id": "7e12b81da5883f4e69cb8901724f6b72",
                        "content": "<text>It is probably not worth dedicating engineering resources to improving that component of the system.</text>"
                    },
                    {
                        "id": "9f053ae4fd1cf04088fa807a899c8a5f",
                        "content": "<text>If that component is a classifier training using gradient descent, it is probably not worth running gradient descent for 10x as long to see if it converges to better classifier parameters.</text>"
                    },
                    {
                        "id": "e2df07c8123571e7205c5fd1fda0d49d",
                        "content": "<text>Choosing more features for that component may help (reducing bias), and reducing the number of features for that component (reducing variance) is unlikely to do so.</text>"
                    }
                ],
                "answer": [
                    "7e12b81da5883f4e69cb8901724f6b72",
                    "9f053ae4fd1cf04088fa807a899c8a5f"
                ],
                "explanation": "",
                "videoCuePoint": 753600
            }
        ]
    },
    {
        "videoId": "Ivxamr1-EeSqHiIAC2idzw",
        "questions": []
    }
]