Mai Chi Bao _ Lab 2 .ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression with a Neural Network mindset\n",
    "\n",
    "Welcome to your first (required) programming assignment! You will build a logistic regression classifier to recognize Politics-Society News. This assignment will step you through how to do this with a Neural Network mindset, and so will also hone your intuitions about deep learning.\n",
    "\n",
    "**Instructions:**\n",
    "- Do not use loops (for/while) in your code, unless the instructions explicitly ask you to do so.\n",
    "\n",
    "**You will learn to:**\n",
    "- Build the general architecture of a learning algorithm, including:\n",
    "    - Initializing parameters\n",
    "    - Calculating the cost function and its gradient\n",
    "    - Using an optimization algorithm (gradient descent) \n",
    "- Gather all three functions above into a main model function, in the right order."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Packages ##\n",
    "\n",
    "First, let's run the cell below to import all the packages that you will need during this assignment. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import pandas as pd\n",
    "from sklearn import model_selection, preprocessing\n",
    "from sklearn.feature_extraction.text import TfidfVectorizer\n",
    "\n",
    "np.random.seed(123) #for reprodicible results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 2 - Dataset preparation ##\n",
    "\n",
    "**Problem Statement**:\n",
    "\n",
    "Bộ data gồm cột text và label. text là câu hỏi, lable là topic của câu hỏi gồm 2 loại là arithmetic và percentages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/mrzaizai2k/code_Bao/Nlp_co5256/venv/lib/python3.10/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n",
      "  from .autonotebook import tqdm as notebook_tqdm\n"
     ]
    }
   ],
   "source": [
    "splits = {'train': 'data/train-00000-of-00001.parquet', 'test': 'data/test-00000-of-00001.parquet'}\n",
    "df = pd.read_parquet(\"hf://datasets/gretelai/synthetic-gsm8k-reflection-405b/\" + splits[\"train\"])\n",
    "df = df[df['topic'].isin(['arithmetic', 'percentages'])]\n",
    "df = df[['topic', 'question']].rename(columns={'topic': 'label', 'question': 'text'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>label</th>\n",
       "      <th>text</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>arithmetic</td>\n",
       "      <td>Tomás wants to buy a new backpack for school t...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>arithmetic</td>\n",
       "      <td>Tomás is planning a school trip from Madrid to...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>percentages</td>\n",
       "      <td>Maria is shopping at a department store during...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>percentages</td>\n",
       "      <td>Yuna is making a traditional Japanese-style me...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>percentages</td>\n",
       "      <td>The Santos family is planning a summer vacatio...</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "          label                                               text\n",
       "1    arithmetic  Tomás wants to buy a new backpack for school t...\n",
       "7    arithmetic  Tomás is planning a school trip from Madrid to...\n",
       "8   percentages  Maria is shopping at a department store during...\n",
       "13  percentages  Yuna is making a traditional Japanese-style me...\n",
       "25  percentages  The Santos family is planning a summer vacatio..."
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The dataframe has two columns, text and label \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of arithmetic documents: 738\n",
      "Number of other documents: 789\n"
     ]
    }
   ],
   "source": [
    "size_politics_society = df[df['label'] == 'arithmetic'].shape[0]\n",
    "size_others = df[df['label'] == 'percentages'].shape[0]\n",
    "print('Number of arithmetic documents: %s' %size_politics_society)\n",
    "print('Number of other documents: %s' %size_others)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Tomás is planning a school trip from Madrid to Paris. He finds a bus tour that costs €800 for a group of 20 students. However, if the group size increases to 25, the cost per student decreases by 10%. How much will each student pay if Tomás decides to invite 5 more students to join the trip?'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# an example of a politics-society news\n",
    "df['text'][7]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we will split the dataset into training and test sets so that we can train and test classifier. Also, we will encode our target column so that it can be used in our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[\"arithmetic\" \"percentages\"] labels corresponds to [0 1] labels\n"
     ]
    }
   ],
   "source": [
    "# split the dataset into training and test datasets \n",
    "train_x, test_x, train_y, test_y =model_selection.train_test_split(df['text'], df['label'])\n",
    "\n",
    "# label encode the target variable, encode labels to 0 or 1\n",
    "encoder = preprocessing.LabelEncoder()\n",
    "train_y = encoder.fit_transform(train_y)\n",
    "test_y = encoder.fit_transform(test_y)\n",
    "print('[\"arithmetic\" \"percentages\"] labels corresponds to %s labels' %encoder.transform([\"arithmetic\", \"percentages\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The next step is the feature engineering step. In this step, raw text data will be transformed into feature vectors and new features will be created using the existing dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TF-IDF Vectors as features\n",
    "TF-IDF score represents the relative importance of a term in the document and the entire corpus. TF-IDF score is composed by two terms: the first computes the normalized Term Frequency (TF), the second term is the Inverse Document Frequency (IDF), computed as the logarithm of the number of the documents in the corpus divided by the number of documents where the specific term appears.\n",
    "\n",
    "TF(t) = (Number of times term t appears in a document) / (Total number of terms in the document)\n",
    "\n",
    "IDF(t) = log_e(Total number of documents / Number of documents with term t in it)\n",
    "\n",
    "TF-IDF Vectors can be generated at different levels of input tokens (words, characters, n-grams)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# word level tf-idf\n",
    "tfidf_vect = TfidfVectorizer(analyzer='word', token_pattern=r'\\w{1,}', max_features=5000)\n",
    "tfidf_vect.fit(df['text'])\n",
    "xtrain_tfidf =  tfidf_vect.transform(train_x)\n",
    "xtest_tfidf =  tfidf_vect.transform(test_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of training documents: 1145\n",
      "Number of testing documents: 382\n",
      "Number of features of each document: 4016\n",
      "xtrain_tfidf shape: (1145, 4016)\n",
      "train_y shape: (1145,)\n",
      "xtest_tfidf shape: (382, 4016)\n",
      "test_y shape: (382,)\n"
     ]
    }
   ],
   "source": [
    "# Getting transformed training and testing dataset\n",
    "print('Number of training documents: %s' %str(xtrain_tfidf.shape[0]))\n",
    "print('Number of testing documents: %s' %str(xtest_tfidf.shape[0]))\n",
    "print('Number of features of each document: %s' %str(xtrain_tfidf.shape[1]))\n",
    "print('xtrain_tfidf shape: %s' %str(xtrain_tfidf.shape))\n",
    "print('train_y shape: %s' %str(train_y.shape))\n",
    "print('xtest_tfidf shape: %s' %str(xtest_tfidf.shape))\n",
    "print('test_y shape: %s' %str(test_y.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many software bugs in deep learning come from having matrix/vector dimensions that don't fit. If you can keep your matrix/vector dimensions straight you will go a long way toward eliminating many bugs.\n",
    "\n",
    "**Exercise:**: For convenience, you should now transpose the training and testing numpy-array, and expand the shape of the lable arrays in the axis=0 position.\n",
    "\n",
    "After this, our training (and test) dataset is a numpy-array where each column represents a document vector. There should be the number of training documents (respectively the number of testing documents) as the number of columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "### START CODE HERE ###\n",
    "train_y = np.expand_dims(train_y, axis=0)\n",
    "test_y = np.expand_dims(test_y, axis=0)\n",
    "\n",
    "# for convenience in this exercise, we also use toarray() to convert sparse to dense matrix \n",
    "xtrain_tfidf =  xtrain_tfidf.T.toarray() \n",
    "xtest_tfidf =  xtest_tfidf.T.toarray()\n",
    "### END CODE HERE ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xtrain_tfidf shape: (4016, 1145)\n",
      "train_y shape: (1, 1145)\n",
      "xtest_tfidf shape: (4016, 382)\n",
      "test_y shape: (1, 382)\n"
     ]
    }
   ],
   "source": [
    "# New shape \n",
    "print('xtrain_tfidf shape: %s' %str(xtrain_tfidf.shape))\n",
    "print('train_y shape: %s' %str(train_y.shape))\n",
    "print('xtest_tfidf shape: %s' %str(xtest_tfidf.shape))\n",
    "print('test_y shape: %s' %str(test_y.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - General Architecture of the learning algorithm ##\n",
    "\n",
    "It's time to design a simple algorithm to distinguish politics-society news from other news.\n",
    "\n",
    "You will build a Logistic Regression, using a Neural Network mindset. The following Figure explains why **Logistic Regression is actually a very simple Neural Network!**\n",
    "\n",
    "**The below image is an analogy of the network architecture of an image classifier to a text classifier.**\n",
    "\n",
    "<img src=\"images/LogReg_kiank.png\" style=\"width:650px;height:400px;\">\n",
    "\n",
    "**Mathematical expression of the algorithm**:\n",
    "\n",
    "For one example $x^{(i)}$:\n",
    "$$z^{(i)} = w^T x^{(i)} + b \\tag{1}$$\n",
    "$$\\hat{y}^{(i)} = a^{(i)} = sigmoid(z^{(i)})\\tag{2}$$ \n",
    "$$ \\mathcal{L}(a^{(i)}, y^{(i)}) =  - y^{(i)}  \\log(a^{(i)}) - (1-y^{(i)} )  \\log(1-a^{(i)})\\tag{3}$$\n",
    "\n",
    "The cost is then computed by summing over all training examples:\n",
    "$$ J = \\frac{1}{m} \\sum_{i=1}^m \\mathcal{L}(a^{(i)}, y^{(i)})\\tag{6}$$\n",
    "\n",
    "**Key steps**:\n",
    "In this exercise, you will carry out the following steps: \n",
    "    - Initialize the parameters of the model\n",
    "    - Learn the parameters for the model by minimizing the cost  \n",
    "    - Use the learned parameters to make predictions (on the test set)\n",
    "    - Analyse the results and conclude"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Building the parts of our algorithm ## \n",
    "\n",
    "The main steps for building a Neural Network are:\n",
    "1. Define the model structure (such as number of input features) \n",
    "2. Initialize the model's parameters\n",
    "3. Loop:\n",
    "    - Calculate current loss (forward propagation)\n",
    "    - Calculate current gradient (backward propagation)\n",
    "    - Update parameters (gradient descent)\n",
    "\n",
    "You often build 1-3 separately and integrate them into one function we call `model()`.\n",
    "\n",
    "### 4.1 - Helper functions\n",
    "\n",
    "**Exercise**: Using your code from \"Python Basics\", implement `sigmoid()`. As you've seen in the figure above, you need to compute $sigmoid( w^T x + b) = \\frac{1}{1 + e^{-(w^T x + b)}}$ to make predictions. Use np.exp()."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: sigmoid\n",
    "\n",
    "def sigmoid(z):\n",
    "    \"\"\"\n",
    "    Compute the sigmoid of z\n",
    "\n",
    "    Arguments:\n",
    "    z -- A scalar or numpy array of any size.\n",
    "\n",
    "    Return:\n",
    "    s -- sigmoid(z)\n",
    "    \"\"\"\n",
    "\n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    s = 1/(1+np.exp(-z))\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sigmoid([0, 2]) = [0.5        0.88079708]\n"
     ]
    }
   ],
   "source": [
    "print (\"sigmoid([0, 2]) = \" + str(sigmoid(np.array([0,2]))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table>\n",
    "  <tr>\n",
    "    <td>**sigmoid([0, 2])**</td>\n",
    "    <td> [ 0.5         0.88079708]</td> \n",
    "  </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 - Initializing parameters\n",
    "\n",
    "**Exercise:** Implement parameter initialization in the cell below. You have to initialize w as a vector of zeros. If you don't know what numpy function to use, look up np.zeros() in the Numpy library's documentation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_with_zeros\n",
    "\n",
    "def initialize_with_zeros(dim):\n",
    "    \"\"\"\n",
    "    This function creates a vector of zeros of shape (dim, 1) for w and initializes b to 0.\n",
    "    \n",
    "    Argument:\n",
    "    dim -- size of the w vector we want (or number of parameters in this case)\n",
    "    \n",
    "    Returns:\n",
    "    w -- initialized vector of shape (dim, 1)\n",
    "    b -- initialized scalar (corresponds to the bias)\n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    w = np.zeros((dim,1))\n",
    "    b = 0.\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    assert(w.shape == (dim, 1))\n",
    "    assert(isinstance(b, float) or isinstance(b, int))\n",
    "    \n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[0.]\n",
      " [0.]]\n",
      "b = 0.0\n"
     ]
    }
   ],
   "source": [
    "dim = 2\n",
    "w, b = initialize_with_zeros(dim)\n",
    "print (\"w = \" + str(w))\n",
    "print (\"b = \" + str(b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "\n",
    "<table style=\"width:15%\">\n",
    "    <tr>\n",
    "        <td>  ** w **  </td>\n",
    "        <td> [[ 0.]\n",
    " [ 0.]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** b **  </td>\n",
    "        <td> 0 </td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 - Forward and Backward propagation\n",
    "\n",
    "Now that your parameters are initialized, you can do the \"forward\" and \"backward\" propagation steps for learning the parameters.\n",
    "\n",
    "**Exercise:** Implement a function `propagate()` that computes the cost function and its gradient.\n",
    "\n",
    "**Hints**:\n",
    "\n",
    "Forward Propagation:\n",
    "- You get X\n",
    "- You compute $A = \\sigma(w^T X + b) = (a^{(1)}, a^{(2)}, ..., a^{(m-1)}, a^{(m)})$\n",
    "- You calculate the cost function: $J = -\\frac{1}{m}\\sum_{i=1}^{m}y^{(i)}\\log(a^{(i)})+(1-y^{(i)})\\log(1-a^{(i)})$\n",
    "\n",
    "Here are the two formulas you will be using: \n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial w} = \\frac{1}{m}X(A-Y)^T\\tag{7}$$\n",
    "$$ \\frac{\\partial J}{\\partial b} = \\frac{1}{m} \\sum_{i=1}^m (a^{(i)}-y^{(i)})\\tag{8}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: propagate\n",
    "\n",
    "def propagate(w, b, X, Y):\n",
    "    \"\"\"\n",
    "    Implement the cost function and its gradient for the propagation explained above\n",
    "\n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (num_px * num_px * 3, number of examples)\n",
    "    Y -- true \"label\" vector of size (1, number of examples)\n",
    "\n",
    "    Return:\n",
    "    cost -- negative log-likelihood cost for logistic regression\n",
    "    dw -- gradient of the loss with respect to w, thus same shape as w\n",
    "    db -- gradient of the loss with respect to b, thus same shape as b\n",
    "    \n",
    "    Tips:\n",
    "    - Write your code step by step for the propagation. np.log(), np.dot()\n",
    "    \"\"\"\n",
    "    \n",
    "    m = float(X.shape[1])\n",
    "    \n",
    "    # FORWARD PROPAGATION (FROM X TO COST)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    A = sigmoid(np.dot(w.T,X) + b)                                    # compute activation\n",
    "    cost = -(1/m) * (np.sum((Y*np.log(A))+ ((1-Y)*np.log(1-A))))     # compute cost\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    # BACKWARD PROPAGATION (TO FIND GRAD)\n",
    "    ### START CODE HERE ### (≈ 2 lines of code)\n",
    "    dw = (1/m)*(np.dot(X,(A-Y).T))\n",
    "    db = (1/m)*(np.sum(A-Y))\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    assert(dw.shape == w.shape)\n",
    "    assert(db.dtype == float)\n",
    "    cost = np.squeeze(cost)\n",
    "    assert(cost.shape == ())\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return grads, cost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dw = [[0.99845601]\n",
      " [2.39507239]]\n",
      "db = 0.001455578136784208\n",
      "cost = 5.801545319394553\n"
     ]
    }
   ],
   "source": [
    "w, b, X, Y = np.array([[1.],[2.]]), 2., np.array([[1.,2.,-1.],[3.,4.,-3.2]]), np.array([[1,0,1]])\n",
    "grads, cost = propagate(w, b, X, Y)\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))\n",
    "print (\"cost = \" + str(cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\">\n",
    "    <tr>\n",
    "        <td>  ** dw **  </td>\n",
    "      <td> [[ 0.99845601]\n",
    "     [ 2.39507239]]</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** db **  </td>\n",
    "        <td> 0.00145557813678 </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>  ** cost **  </td>\n",
    "        <td> 5.801545319394553 </td>\n",
    "    </tr>\n",
    "\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 - Optimization\n",
    "- You have initialized your parameters.\n",
    "- You are also able to compute a cost function and its gradient.\n",
    "- Now, you want to update the parameters using gradient descent.\n",
    "\n",
    "**Exercise:** Write down the optimization function. The goal is to learn $w$ and $b$ by minimizing the cost function $J$. For a parameter $\\theta$, the update rule is $ \\theta = \\theta - \\alpha \\text{ } d\\theta$, where $\\alpha$ is the learning rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: optimize\n",
    "\n",
    "def optimize(w, b, X, Y, num_iterations, learning_rate, print_cost = False):\n",
    "    \"\"\"\n",
    "    This function optimizes w and b by running a gradient descent algorithm\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of shape (num_px * num_px * 3, number of examples)\n",
    "    Y -- true \"label\" vector, of shape (1, number of examples)\n",
    "    num_iterations -- number of iterations of the optimization loop\n",
    "    learning_rate -- learning rate of the gradient descent update rule\n",
    "    print_cost -- True to print the loss every 100 steps\n",
    "    \n",
    "    Returns:\n",
    "    params -- dictionary containing the weights w and bias b\n",
    "    grads -- dictionary containing the gradients of the weights and bias with respect to the cost function\n",
    "    costs -- list of all the costs computed during the optimization, this will be used to plot the learning curve.\n",
    "    \n",
    "    Tips:\n",
    "    You basically need to write down two steps and iterate through them:\n",
    "        1) Calculate the cost and the gradient for the current parameters. Use propagate().\n",
    "        2) Update the parameters using gradient descent rule for w and b.\n",
    "    \"\"\"\n",
    "    \n",
    "    costs = []\n",
    "    \n",
    "    for i in range(num_iterations):\n",
    "        \n",
    "        \n",
    "        # Cost and gradient calculation (≈ 1-4 lines of code)\n",
    "        ### START CODE HERE ### \n",
    "        grads, cost = propagate(w,b,X,Y)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Retrieve derivatives from grads\n",
    "        dw = grads[\"dw\"]\n",
    "        db = grads[\"db\"]\n",
    "        \n",
    "        # update rule (≈ 2 lines of code)\n",
    "        ### START CODE HERE ###\n",
    "        w = w - learning_rate*dw\n",
    "        b = b - learning_rate*db\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "        # Record the costs\n",
    "        if i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "        \n",
    "        # Print the cost every 100 training iterations\n",
    "        if print_cost and i % 100 == 0:\n",
    "            print (\"Cost after iteration %i: %f\" %(i, cost))\n",
    "    \n",
    "    params = {\"w\": w,\n",
    "              \"b\": b}\n",
    "    \n",
    "    grads = {\"dw\": dw,\n",
    "             \"db\": db}\n",
    "    \n",
    "    return params, grads, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w = [[0.19033591]\n",
      " [0.12259159]]\n",
      "b = 1.9253598300845747\n",
      "dw = [[0.67752042]\n",
      " [1.41625495]]\n",
      "db = 0.21919450454067657\n"
     ]
    }
   ],
   "source": [
    "params, grads, costs = optimize(w, b, X, Y, num_iterations= 100, learning_rate = 0.009, print_cost = False)\n",
    "\n",
    "print (\"w = \" + str(params[\"w\"]))\n",
    "print (\"b = \" + str(params[\"b\"]))\n",
    "print (\"dw = \" + str(grads[\"dw\"]))\n",
    "print (\"db = \" + str(grads[\"db\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:40%\">\n",
    "    <tr>\n",
    "       <td> **w** </td>\n",
    "       <td>[[ 0.19033591] [ 0.12259159]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **b** </td>\n",
    "       <td> 1.92535983008 </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **dw** </td>\n",
    "       <td> [[ 0.67752042] [ 1.41625495]] </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "       <td> **db** </td>\n",
    "       <td> 0.219194504541 </td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** The previous function will output the learned w and b. We are able to use w and b to predict the labels for a dataset X. Implement the `predict()` function. There are two steps to computing predictions:\n",
    "\n",
    "1. Calculate $\\hat{Y} = A = \\sigma(w^T X + b)$\n",
    "\n",
    "2. Convert the entries of a into 0 (if activation <= 0.5) or 1 (if activation > 0.5), stores the predictions in a vector `Y_prediction`. If you wish, you can use an `if`/`else` statement in a `for` loop (though there is also a way to vectorize this). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: predict\n",
    "\n",
    "def predict(w, b, X):\n",
    "    '''\n",
    "    Predict whether the label is 0 or 1 using learned logistic regression parameters (w, b)\n",
    "    \n",
    "    Arguments:\n",
    "    w -- weights, a numpy array of size (num_px * num_px * 3, 1)\n",
    "    b -- bias, a scalar\n",
    "    X -- data of size (num_px * num_px * 3, number of examples)\n",
    "    \n",
    "    Returns:\n",
    "    Y_prediction -- a numpy array (vector) containing all predictions (0/1) for the examples in X\n",
    "    '''\n",
    "    \n",
    "    m = X.shape[1]\n",
    "    Y_prediction = np.zeros((1,m), dtype=int)\n",
    "    w = w.reshape(X.shape[0], 1)\n",
    "    \n",
    "    # Compute vector \"A\" predicting the probabilities of a news being present\n",
    "    ### START CODE HERE ### (≈ 1 line of code)\n",
    "    A = sigmoid(np.dot(w.T,X) + b)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    for i in range(A.shape[1]):\n",
    "        # Convert probabilities A[0,i] to actual predictions p[0,i]\n",
    "        ### START CODE HERE ### (≈ 4 lines of code)\n",
    "        if (A[0][i] > 0.5):\n",
    "            Y_prediction[0][i] = 1\n",
    "        else:\n",
    "            Y_prediction[0][i] = 0\n",
    "        ### END CODE HERE ###\n",
    "    \n",
    "    assert(Y_prediction.shape == (1, m))\n",
    "    \n",
    "    return Y_prediction, A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predictions = [[1 1 0]]\n"
     ]
    }
   ],
   "source": [
    "w = np.array([[0.1124579],[0.23106775]])\n",
    "b = -0.3\n",
    "X = np.array([[1.,-1.1,-3.2],[1.2,2.,0.1]])\n",
    "print (\"predictions = \" + str(predict(w, b, X)[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**: \n",
    "\n",
    "<table style=\"width:30%\">\n",
    "    <tr>\n",
    "         <td>\n",
    "             **predictions**\n",
    "         </td>\n",
    "          <td>\n",
    "            [[ 1.  1.  0.]]\n",
    "         </td>  \n",
    "   </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<font color='blue'>\n",
    "**What to remember:**\n",
    "You've implemented several functions that:\n",
    "- Initialize (w,b)\n",
    "- Optimize the loss iteratively to learn parameters (w,b):\n",
    "    - computing the cost and its gradient \n",
    "    - updating the parameters using gradient descent\n",
    "- Use the learned (w,b) to predict the labels for a given set of examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Merge all functions into a model ##\n",
    "\n",
    "You will now see how the overall model is structured by putting together all the building blocks (functions implemented in the previous parts) together, in the right order.\n",
    "\n",
    "**Exercise:** Implement the model function. Use the following notation:\n",
    "    - Y_prediction_test for your predictions on the test set\n",
    "    - Y_prediction_train for your predictions on the train set\n",
    "    - w, costs, grads for the outputs of optimize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: model\n",
    "\n",
    "def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):\n",
    "    \"\"\"\n",
    "    Builds the logistic regression model by calling the function you've implemented previously\n",
    "    \n",
    "    Arguments:\n",
    "    X_train -- training set represented by a numpy array of shape (num_px * num_px * 3, m_train)\n",
    "    Y_train -- training labels represented by a numpy array (vector) of shape (1, m_train)\n",
    "    X_test -- test set represented by a numpy array of shape (num_px * num_px * 3, m_test)\n",
    "    Y_test -- test labels represented by a numpy array (vector) of shape (1, m_test)\n",
    "    num_iterations -- hyperparameter representing the number of iterations to optimize the parameters\n",
    "    learning_rate -- hyperparameter representing the learning rate used in the update rule of optimize()\n",
    "    print_cost -- Set to true to print the cost every 100 iterations\n",
    "    \n",
    "    Returns:\n",
    "    d -- dictionary containing information about the model.\n",
    "    \"\"\"\n",
    "    \n",
    "    ### START CODE HERE ###\n",
    "    \n",
    "    # initialize parameters with zeros (≈ 1 line of code)\n",
    "    w, b = initialize_with_zeros(X_train.shape[0])\n",
    "\n",
    "    # Gradient descent (≈ 1 line of code)\n",
    "    parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)\n",
    "    \n",
    "    # Retrieve parameters w and b from dictionary \"parameters\"\n",
    "    w = parameters[\"w\"]\n",
    "    b = parameters[\"b\"]\n",
    "    \n",
    "    # Predict test/train set examples (≈ 2 lines of code)\n",
    "    Y_prediction_test = predict(w,b,X_test)[0]\n",
    "    Y_prediction_train = predict(w,b,X_train)[0]\n",
    "\n",
    "    ### END CODE HERE ###\n",
    "\n",
    "    # Print train/test Errors\n",
    "    print(\"train accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))\n",
    "    print(\"test accuracy: {} %\".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))\n",
    "\n",
    "    \n",
    "    d = {\"costs\": costs,\n",
    "         \"Y_prediction_test\": Y_prediction_test, \n",
    "         \"Y_prediction_train\" : Y_prediction_train, \n",
    "         \"w\" : w, \n",
    "         \"b\" : b,\n",
    "         \"learning_rate\" : learning_rate,\n",
    "         \"num_iterations\": num_iterations}\n",
    "    \n",
    "    return d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run the following cell to train your model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after iteration 0: 0.693147\n",
      "Cost after iteration 100: 0.612154\n",
      "Cost after iteration 200: 0.557682\n",
      "Cost after iteration 300: 0.518383\n",
      "Cost after iteration 400: 0.488477\n",
      "Cost after iteration 500: 0.464703\n",
      "Cost after iteration 600: 0.445133\n",
      "Cost after iteration 700: 0.428574\n",
      "Cost after iteration 800: 0.414254\n",
      "Cost after iteration 900: 0.401653\n",
      "Cost after iteration 1000: 0.390407\n",
      "Cost after iteration 1100: 0.380256\n",
      "Cost after iteration 1200: 0.371006\n",
      "Cost after iteration 1300: 0.362511\n",
      "Cost after iteration 1400: 0.354659\n",
      "Cost after iteration 1500: 0.347360\n",
      "Cost after iteration 1600: 0.340542\n",
      "Cost after iteration 1700: 0.334147\n",
      "Cost after iteration 1800: 0.328127\n",
      "Cost after iteration 1900: 0.322441\n",
      "Cost after iteration 2000: 0.317055\n",
      "Cost after iteration 2100: 0.311941\n",
      "Cost after iteration 2200: 0.307073\n",
      "Cost after iteration 2300: 0.302429\n",
      "Cost after iteration 2400: 0.297991\n",
      "Cost after iteration 2500: 0.293742\n",
      "Cost after iteration 2600: 0.289667\n",
      "Cost after iteration 2700: 0.285754\n",
      "Cost after iteration 2800: 0.281990\n",
      "Cost after iteration 2900: 0.278365\n",
      "train accuracy: 92.48908296943232 %\n",
      "test accuracy: 87.95811518324608 %\n"
     ]
    }
   ],
   "source": [
    "d = model(xtrain_tfidf, train_y, xtest_tfidf, test_y, num_iterations = 3000, learning_rate = .5, print_cost = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Comment**: Training accuracy is close to 100%. This is a good sanity check: your model is working and has high enough capacity to fit the training data. Test error is around 84%. It is actually not bad for this simple model, given the small dataset we used and that logistic regression is a linear classifier. You'll build an even better classifier next week!\n",
    "\n",
    "Also, you see that the model is clearly overfitting the training data. Later in this specialization you will learn how to reduce overfitting, for example by using regularization. Using the code below (and changing the `index` variable) you can look at predictions on pictures of the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ana's family is preparing for the Día de los Muertos celebration. She wants to buy marigolds, her grandmother's favorite flowers, which are on sale with a 15% discount. If the original price of a bouquet is $20, and Ana plans to buy 3 bouquets, how much will she pay in total after applying the discount?\n"
     ]
    }
   ],
   "source": [
    "# Example of a news that was wrongly classified.\n",
    "index = 1\n",
    "print(list(test_x[index:index+1])[0])\n",
    "true = test_y[0][index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ana's family is preparing for the Día de los Muertos celebration. She wants to buy marigolds, her grandmother's favorite flowers, which are on sale with a 15% discount. If the original price of a bouquet is $20, and Ana plans to buy 3 bouquets, how much will she pay in total after applying the discount?\n",
      "------------------------------------------------------------\n",
      "This is \"['percentages']\" news, you predicted it is \"['percentages']\" news\n"
     ]
    }
   ],
   "source": [
    "# Example of a news that was wrongly classified.\n",
    "index = 1\n",
    "print(list(test_x[index:index+1])[0])\n",
    "true = test_y[0][index]\n",
    "pred = d['Y_prediction_test'][0][index]\n",
    "print('------------------------------------------------------------')\n",
    "print('This is \"%s\" news, you predicted it is \"%s\" news' %(encoder.inverse_transform([true]), encoder.inverse_transform([pred])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also plot the cost function and the gradients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot learning curve (with costs)\n",
    "costs = np.squeeze(d['costs'])\n",
    "plt.plot(costs)\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (per hundreds)')\n",
    "plt.title(\"Learning rate =\" + str(d[\"learning_rate\"]))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Interpretation**:\n",
    "You can see the cost decreasing. It shows that the parameters are being learned. However, you see that you could train the model even more on the training set. Try to increase the number of iterations in the cell above and rerun the cells. You might see that the training set accuracy goes up, but the test set accuracy goes down. This is called overfitting. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6 - Further analysis (optional/ungraded exercise) ##\n",
    "\n",
    "Congratulations on building your first text classification model. Let's analyze it further, and examine possible choices for the learning rate $\\alpha$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Choice of learning rate ####\n",
    "\n",
    "**Reminder**:\n",
    "In order for Gradient Descent to work you must choose the learning rate wisely. The learning rate $\\alpha$  determines how rapidly we update the parameters. If the learning rate is too large we may \"overshoot\" the optimal value. Similarly, if it is too small we will need too many iterations to converge to the best values. That's why it is crucial to use a well-tuned learning rate.\n",
    "\n",
    "Let's compare the learning curve of our model with several choices of learning rates. Run the cell below. This should take about 1 minute. Feel free also to try different values than the three we have initialized the `learning_rates` variable to contain, and see what happens. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "learning rate is: 0.01\n",
      "train accuracy: 83.23144104803494 %\n",
      "test accuracy: 80.89005235602095 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.1\n",
      "train accuracy: 85.67685589519651 %\n",
      "test accuracy: 82.98429319371728 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n",
      "learning rate is: 0.5\n",
      "train accuracy: 92.48908296943232 %\n",
      "test accuracy: 87.95811518324608 %\n",
      "\n",
      "-------------------------------------------------------\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rates = [0.01, 0.1, 0.5]\n",
    "models = {}\n",
    "for i in learning_rates:\n",
    "    print (\"learning rate is: \" + str(i))\n",
    "    models[str(i)] = model(xtrain_tfidf, train_y, xtest_tfidf, test_y, num_iterations = 3000, learning_rate = i, print_cost = False)\n",
    "    print ('\\n' + \"-------------------------------------------------------\" + '\\n')\n",
    "\n",
    "for i in learning_rates:\n",
    "    plt.plot(np.squeeze(models[str(i)][\"costs\"]), label= str(models[str(i)][\"learning_rate\"]))\n",
    "\n",
    "plt.ylabel('cost')\n",
    "plt.xlabel('iterations (hundreds)')\n",
    "\n",
    "legend = plt.legend(loc='upper center', shadow=True)\n",
    "frame = legend.get_frame()\n",
    "frame.set_facecolor('0.90')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Interpretation**: \n",
    "- Different learning rates give different costs and thus different predictions results.\n",
    "- If the learning rate is too large, the cost may oscillate up and down. It may even diverge (though in this example, using 0.5 does not have that problem and still eventually ends up at a good value for the cost). \n",
    "- A lower cost doesn't mean a better model. You have to check if there is possibly overfitting. It happens when the training accuracy is a lot higher than the test accuracy.\n",
    "- In deep learning, we usually recommend that you: \n",
    "    - Choose the learning rate that better minimizes the cost function.\n",
    "    - If your model overfits, use other techniques to reduce overfitting. (We'll talk about this in later videos.) \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 7 - Test with your own news (optional/ungraded exercise) ##\n",
    "\n",
    "Congratulations on finishing this assignment. You can use your own text and see the output of your model.\n",
    "\n",
    "[\"Chinhtrixahoi\" \"percentages\"] labels corresponds to [0 1] labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "text = \"\"\"Sarah is buying pencils for her class. She finds a store where a pack of 12 pencils costs $6. If the store offers \n",
    "a 15% discount on each pack for purchases of 5 packs or more, how much will Sarah pay in total if she buys 5 packs of pencils?\n",
    "\"\"\"\n",
    "\n",
    "x_tfidf =  tfidf_vect.transform([text]).T.toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1]]), array([[0.53488581]]))"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predict(d[\"w\"], d[\"b\"], x_tfidf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What to remember from this assignment:**\n",
    "1. Preprocessing the dataset is important.\n",
    "2. You implemented each function separately: initialize(), propagate(), optimize(). Then you built a model().\n",
    "3. Tuning the learning rate (which is an example of a \"hyperparameter\") can make a big difference to the algorithm. You will see more examples of this later in this course!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, if you'd like, we invite you to try different things on this Notebook. Make sure you submit before trying anything. Once you submit, things you can play with include:\n",
    "    - Play with the learning rate and the number of iterations\n",
    "    - Try different initialization methods and compare the results\n",
    "    - Test other preprocessings \n",
    "    - Try others parameters of TfidfVectorizer, such as ngrams, lowercase\n",
    "    - See what features are in a Tf-idf vector\n",
    "    - Test with different feature representation other than Tf-idf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bibliography:\n",
    "- http://www.wildml.com/2015/09/implementing-a-neural-network-from-scratch/\n",
    "- https://stats.stackexchange.com/questions/211436/why-do-we-normalize-images-by-subtracting-the-datasets-image-mean-and-not-the-c"
   ]
  }
 ],
 "metadata": {
  "coursera": {
   "course_slug": "neural-networks-deep-learning",
   "graded_item_id": "XaIWT",
   "launcher_item_id": "zAgPl"
  },
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
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