01_intro_AI_on_Supercomputer/01_linear_regression_sgd.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Artificial intelligence in a nutshell\n",
    "\n",
    "In this notebook, we will talk about \n",
    "* What is AI training? \n",
    "* How does large language model work? \n",
    "* A simple AI model: linear regression\n",
    "\n",
    "**How to run this notebook on Polaris**\n",
    "* Go to https://jupyter.alcf.anl.gov, and click \"Login Polaris\"\n",
    "* After login, select ```ALCFAITP``` project and ```ALCFAITP``` queue\n",
    "* Load the notebook and select \"datascience/conda-2023-01-10\" python kernel\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/jupyter1.png\" width=\"600\" />\n",
    "  <img src=\"figures/jupyter2.png\" width=\"600\" /> \n",
    "</p>\n",
    "\n",
    "**How to run this notebook on Google Colab**\n",
    "\n",
    "* Go to https://colab.research.google.com/, sign in or sign up\n",
    "* \"File\"-> \"open notebook\"\n",
    "* choose ```01_intro_AI_on_Supercomputer/01_linear_regression_sgd.ipynb``` from the list\n",
    "![Google Colab](figures/colab.png)\n",
    "\n",
    "## What is AI training?\n",
    "**Two ways of learning English** \n",
    "* through learning rules;\n",
    "* through hearing a lot of speakings\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/data_driven.png\" width=\"1000\" /> \n",
    "</p>\n",
    "\n",
    "I learned English in my middle school, and memorized a lot of grammar rules in my mind. Every time when I speak, I try to follow the grammar rules as much as I can. But I always break the rules. \n",
    "\n",
    "However, my daugher Phoebe learned English differently. She learns speaking by hearing a lot of speaking from TV, teachers, classmates, and her older brother Nehemiah. The fact is that, she seldomly breaks grammar rules. This way of learning by observing patterns is very powerful! This is the essence of AI or data driven science. \n",
    "\n",
    "## How does large language model work? \n",
    "\n",
    "Large Language Models, like GPT, function by pre-training on extensive datasets to learn language patterns, utilizing transformer architecture for contextual understanding, and can be fine-tuned for specific tasks, enabling them to generate coherent and contextually relevant text based on provided inputs.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/LLM.png\" width=\"600\" />\n",
    "  <img src=\"figures/chatgpt_response.png\" width=\"160\" /> \n",
    "</p>\n",
    "\n",
    "**More complicated example**\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/chatgpt_poem.png\" width=\"400\" /> \n",
    "  <img src=\"figures/martin.png\" width=\"450\" /> \n",
    "</p>\n",
    "\n",
    "You can do this on https://chat.openai.com\n",
    "\n",
    "## Simplest AI model example: linear regression\n",
    "This example is adopted from Bethany Lusch, ALCF. \n",
    "\n",
    "Linear regression is the simplest example ``learning\" from existing data for future prediction. \n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/excel_linear_regression.jpg\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "We're going to review the math involved in this process to help understand how training an AI works.\n",
    "\n",
    "First we will load some tools that others wrote and we can use to help us work.\n",
    "* [Pandas](https://pandas.pydata.org/docs/): a toolkit for working with row vs. column data, like excel sheets, and CSV (Comma Seperated Values) files.\n",
    "* [Numpy](https://numpy.org/doc/): a toolkit for managing arrays, vectors, matrices, etc, doing math with them, slicing them up, and many other handy things.\n",
    "* [Matplotlib](https://matplotlib.org/stable/index.html): a toolkit for plotting data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import IPython.display as ipydis\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dataset\n",
    "We used a realestate dataset from Kaggle to produce this reduced dataset. This dataset contains the _sale price_ and _above ground square feet_ of many houses. We can use this data for our linear regression.\n",
    "\n",
    "We use Pandas to read the data file which is stored as Comma Separated Values (CSV). and print the column labels. CSV files are similar to excel sheets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['Unnamed: 0', 'SalePrice', 'GrLivArea'], dtype='object')\n"
     ]
    }
   ],
   "source": [
    "! [ -e ./slimmed_realestate_data.csv ] || wget https://raw.githubusercontent.com/argonne-lcf/ai-science-training-series/main/01_intro_AI_on_Supercomputer/slimmed_realestate_data.csv\n",
    "data = pd.read_csv('slimmed_realestate_data.csv')\n",
    "print(data.columns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now pandas provides some helpful tools for us to inspect our data. It provides a `plot()` function that, behind the scenes, is calling into the _Matplotlib_ library and calling the function [matplotlib.pyplot.plot()](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html). In this case, we simply tell it the names of the columns we want as our _x_ and _y_ values and the `style` (`'.'` tells `matplotlib` to use a small dot to represent each data point)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot: xlabel='GrLivArea'>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data.plot(x='GrLivArea', y='SalePrice',style='.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Theory of linear regression\n",
    "\n",
    "The goal of learning regression is to find a line that is closest to all the points. \n",
    "\n",
    "The slope and intercept of such a line $y = m x + b$ can be found as: \n",
    "\n",
    "They are:\n",
    "\n",
    "$$m = { n (\\Sigma xy) - (\\Sigma x) (\\Sigma y) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "$$b = { (\\Sigma y) (\\Sigma x^2) - (\\Sigma x) (\\Sigma xy) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\n",
    "\n",
    "Details derivation of this can be found [here](https://en.wikipedia.org/wiki/Simple_linear_regression). \n",
    "\n",
    "We'll break this calculation into a few steps to help make it easier.\n",
    "\n",
    "First lets define $x$ and $y$. $x$ will be our _above ground square footage_ and $y$ will be _sale price_. In our equations we have a few different values we need, such as $n$ which is just the number of points we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we need our $x$ and $y$ by selecting only the column we care about for each one. Note about data formats: `data` is a Pandas [DataFrame](https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.html#pandas.DataFrame) object which has rows and columns; `data['GrLivArea']` is a Pandas [Series](https://pandas.pydata.org/docs/reference/api/pandas.Series.html) object which only has rows; then we also convert from _Pandas_ data formats (in this case a _Series_) to _Numpy_ data formats using the `to_numpy()` function which is part of the Pandas _Series_ object. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data['GrLivArea'].to_numpy()\n",
    "y = data['SalePrice'].to_numpy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we will calculate $\\Sigma xy$, $\\Sigma x$, $\\Sigma y$, and $\\Sigma x^2$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "sum_xy = np.sum(x*y)\n",
    "sum_x = np.sum(x)\n",
    "sum_y = np.sum(y)\n",
    "sum_x2 = np.sum(x*x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The denominator in the equation for $m$ and $b$ are the same so we can calculate that once:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "denominator = n * sum_x2 - sum_x * sum_x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our fit values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y = 87.688145 * x + 34754.077892\n"
     ]
    }
   ],
   "source": [
    "m = (n * sum_xy - sum_x * sum_y) / denominator\n",
    "b = (sum_y * sum_x2 - sum_x * sum_xy) / denominator\n",
    "print('y = %f * x + %f' % (m,b))\n",
    "\n",
    "# saving these for later comparison\n",
    "m_calc = m\n",
    "b_calc = b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can plot the fit results with our data to see how we did. \n",
    "\n",
    "First we define a plotting function because we're going to do this often and we want to reuse our code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x,y,m,b,plt = plt):\n",
    "   # plot our data points with 'bo' = blue circles\n",
    "   plt.plot(x,y,'bo')\n",
    "   # create the line based on our linear fit\n",
    "   # first we need to make x points\n",
    "   # the 'arange' function generates points between two limits (min,max)\n",
    "   linear_x = np.arange(x.min(),x.max())\n",
    "   # now we use our fit parameters to calculate the y points based on our x points\n",
    "   linear_y = linear_x * m + b\n",
    "   # plot the linear points using 'r-' = red line\n",
    "   plt.plot(linear_x,linear_y,'r-',label='fit')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now can use this function to plot our results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training through Stochastic Gradient Descent (SGD)\n",
    "\n",
    "SGD is a common method in AI for training deep neural networks on large datasets. It is an iterative method for optimizing a loss function that we get to define. We will use this simple linear regression to demonstrate how it works.\n",
    "\n",
    "#### The model\n",
    "\n",
    "In AI, neural networks are often referred to as a _model_ because, once fully trained, they should model (AKA predict) the behavior of our system. In our example, the system is how house prices vary based on house size. We know our system is roughly driven by a linear function:\n",
    "\n",
    "$$ \\hat{y_i}(x_i) = m * x_i + b $$\n",
    "\n",
    "We just need to figure out $m$ and $b$. Let's create a function that calculates our model given $x$, $m$, and $b$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model(x,m,b):\n",
    "   return m * x + b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "\n",
    "#### The Loss Function\n",
    "\n",
    "A _loss function_, or _objective function_, is something we define and is based on what we want to achieve. In the method of SGD, it is our goal to minimize (or make close to zero) the values calculated from the _loss function_. In our example, we ideally want the prediction of our _model_ to be equal to the actual data, though we will settle for \"as close as possible\".\n",
    "\n",
    "So we will select our _loss function_ to be the [Mean Squared Error](https://en.wikipedia.org/wiki/Mean_squared_error) function:\n",
    "\n",
    "$$ L(y_i,\\hat{y_i}) = (y_i - \\hat{y_i}(x_i))^2 $$\n",
    "\n",
    "where $y_i$ is our $i^{th}$ entry in the `data['SalePrice']` vector and $\\hat{y_i}$ is the prediction based on evaluting $m * x_i + b$.\n",
    "\n",
    "This function looks like the figure below when we plot it with $x=y_i - \\hat{y_i}(x_i)$ and we we want to be down near $y_i - \\hat{y_i}(x_i) = 0$ which indicates that our $y_i$ is as close as possible to $\\hat{y_i}$.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/loss_func.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Here we crate a function that calculates this for us."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(x,y,m,b):\n",
    "   y_predicted = model(x,m,b)\n",
    "   return np.power( y - y_predicted, 2 )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Minimizing the Loss Function\n",
    "\n",
    "We want to use the loss function in order to guide how to update $m$ and $b$ to better model our system. In calculus we learn to minimize a function with respect to a variable you calculate the _partial derivative_ with respect to the variable you want to vary.\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = 0 $$\n",
    "\n",
    "The location of the solution to this is the minimum as shown in the figure above. We can write down the partial derivative of the loss function as:\n",
    "\n",
    "$$ { \\partial L \\over \\partial m } = -2 x_i (y_i - \\hat{y_i}(x_i)) $$\n",
    "$$ { \\partial L \\over \\partial b } = -2 (y_i - \\hat{y_i}(x_i)) $$\n",
    "\n",
    "We can use this to calculate an adjustment to $m$ and $b$ that will reduce the loss function, effectively improving our fitting parameters. This is done using this equation:\n",
    "\n",
    "$$ m' = m - \\eta { \\partial L \\over \\partial m }$$\n",
    "$$ b' = b - \\eta { \\partial L \\over \\partial b }$$\n",
    "\n",
    "Here our original $m$ and $b$ are adjusted by the partial derivative multiplied by some small factor, $\\eta$, called the _learning rate_. This learning rate is very important in our process and must be tuned for every problem.\n",
    "\n",
    "In our example, the selection of the learning rate essentially defines how close we can get to the minimum, AKA the best fit solution. This figure shows what happens when we pick a large learning rate. We first select a starting point in our loss function (typically randomly), then every update from $m$/$b$ to $m'$/$b'$ results in a shift to somewhere else on our loss function (following the red arrows). In this example, our learning rate ($\\eta$) has been selected too large such that we bounce back and forth around the minimum, never reaching it.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/parabola_largeLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "If we select a smaller learning we can see better behavior in the next figure.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/parabola_smallLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Though, keep in mind, too small a learning rate results is so little progress toward the minimum that you may never reach it!\n",
    "\n",
    "A pit fall of SGD that one must be aware of is when your loss function is complex, with many minima. The next figure shows such a case, in which we select a small learning rate and our starting point happens to be near a local minimum that is not the lowest minimum. As shown, we do reach a minimum, but it isn't the lowest minimum in our loss function. It could be that we randomly select a starting point near the minimum we care about, but we should build methods that are more robust against randomly getting the right answer.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_smallLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "Then, if we increase our learning rate too much, we bounce around again.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_largeLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "What we want to do in this situation is start with a large learning rate and slowly reduce its size as we progress. That is shown in this next figure.\n",
    "\n",
    "<p float=\"center\">\n",
    "  <img src=\"figures/local_min_variableLR.png\" width=\"400\" /> \n",
    "</p>\n",
    "\n",
    "As you can see, this process is not perfect and could still land in a local minimum, but it is important to be aware of these behaviors as you utilize SGD in machine learning.\n",
    "\n",
    "So let's continue, we'll build functions we can use to update our fit parameters, $m$ and $b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def updated_m(x,y,m,b,learning_rate):\n",
    "   dL_dm = - 2 * x * (y - model(x,m,b))\n",
    "   dL_dm = np.mean(dL_dm)\n",
    "   return m - learning_rate * dL_dm\n",
    "\n",
    "def updated_b(x,y,m,b,learning_rate):\n",
    "   dL_db = - 2 * (y - model(x,m,b))\n",
    "   dL_db = np.mean(dL_db)\n",
    "   return b - learning_rate * dL_db"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Putting it together\n",
    "\n",
    "We can now randomly select our initial slope and intercept:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.00 * x + 1000.00\n"
     ]
    }
   ],
   "source": [
    "m = 5.\n",
    "b = 1000.\n",
    "print('y_i = %.2f * x + %.2f' % (m,b))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can calculate our Loss function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "first 10 loss values:  [3.03421561e+10 3.55511025e+10 1.24579082e+10 1.91656336e+10\n",
      " 1.60604929e+10 2.04432804e+10 1.72410030e+10 1.76517796e+10\n",
      " 1.52769600e+10 2.18152900e+10]\n"
     ]
    }
   ],
   "source": [
    "l = loss(x,y,m,b)\n",
    "print('first 10 loss values: ',l[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y_i = 5.47 * x + 1000.00     previously calculated: y_i = 87.69 * x + 34754.08\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learning_rate = 1e-9\n",
    "m = updated_m(x,y,m,b,learning_rate)\n",
    "b = updated_b(x,y,m,b,learning_rate)\n",
    "print('y_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f' % (m,b,m_calc,b_calc))\n",
    "plot_data(x,y,m,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[014]  dy_i = 89.31 * x + 32264.10     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478547535.979891\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# set our initial slope and intercept\n",
    "m = 5.\n",
    "b = 1000.\n",
    "# batch_size = 60\n",
    "# set a learning rate for each parameter\n",
    "learning_rate_m = 1e-7\n",
    "learning_rate_b = 1e-1\n",
    "# use these to plot our progress over time\n",
    "loss_history = []\n",
    "# convert panda data to numpy arrays, one for the \"Ground Living Area\" and one for \"Sale Price\"\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "# we run our loop N times\n",
    "loop_N = 30\n",
    "for i in range(loop_N):\n",
    "   # update our slope and intercept based on the current values\n",
    "   m = updated_m(data_x,data_y,m,b,learning_rate_m)\n",
    "   b = updated_b(data_x,data_y,m,b,learning_rate_b)\n",
    "\n",
    "   # calculate the loss value\n",
    "   loss_value = np.mean(loss(data_x,data_y,m,b))\n",
    "\n",
    "   # keep a history of our loss values\n",
    "   loss_history.append(loss_value)\n",
    "\n",
    "   # print our progress\n",
    "   print('[%03d]  dy_i = %.2f * x + %.2f     previously calculated: y_i = %.2f * x + %.2f    loss: %f' % (i,m,b,m_calc,b_calc,loss_value))\n",
    "   \n",
    "   # close/delete previous plots\n",
    "   plt.close('all')\n",
    "   \n",
    "   # create a 1 by 2 plot grid\n",
    "   fig,ax = plt.subplots(1,2,figsize=(18,6),dpi=80)\n",
    "   # lot our usual output\n",
    "   plot_data(data_x,data_y,m,b,ax[0])\n",
    "\n",
    "   # here we also plot the calculated linear fit for comparison\n",
    "   line_x = np.arange(data_x.min(),data_x.max())\n",
    "   line_y = line_x * m_calc + b_calc\n",
    "   ax[0].plot(line_x,line_y,'b-',label='calculated')\n",
    "   # add a legend to the plot and x/y labels\n",
    "   ax[0].legend()\n",
    "   ax[0].set_xlabel('square footage')\n",
    "   ax[0].set_ylabel('sale price')\n",
    "\n",
    "   # plot the loss \n",
    "   loss_x = np.arange(0,len(loss_history))\n",
    "   loss_y = np.asarray(loss_history)\n",
    "   ax[1].plot(loss_x,loss_y, 'o-')\n",
    "   ax[1].set_yscale('log')\n",
    "   ax[1].set_xlabel('loop step')\n",
    "   ax[1].set_ylabel('loss')\n",
    "   plt.show()\n",
    "   # gives us time to see the plot\n",
    "   time.sleep(2.5)\n",
    "   # clears the plot when the next plot is ready to show.\n",
    "   ipydis.clear_output(wait=True)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework\n",
    "## Mini Batch Training\n",
    "In AI, datasets are often very large and cannot be processed all at once as is done in the loop above. The data is instead randomly sampled in smaller _batches_ where each _batch_ contains `batch_size` inputs. How can you change the loop above to sample the dataset in smaller batches? Hint: Our `data` variable is a Pandas `DataFrame` object, search for \"how to sample a DataFrame\".\n",
    "\n",
    "Instead of using the entire dataset like \n",
    "```python\n",
    "data_x = data['GrLivArea'].to_numpy()\n",
    "data_y = data['SalePrice'].to_numpy()\n",
    "```\n",
    "Use \n",
    "```python\n",
    "data_batch = data.sample(batch_size)\n",
    "data_x = data_batch['GrLivArea'].to_numpy()\n",
    "data_y = data_batch['SalePrice'].to_numpy()\n",
    "```\n",
    "\n",
    "You also have to adjust the loop_N accordingly to make sure that it loop over the entire datasets the same number of times.\n",
    "```python\n",
    "loop_N = 30*(len(data['GrLivArea'])//batch_size\n",
    "```\n",
    "\n",
    "Please plot your learning curve for different batch size, such as 32, 64, 128, 256, 512. \n",
    "\n",
    "## Learning rate issue (Bonus)\n",
    "As described above, if the learning rate is too large, it will affect the convergence. Do your training with (batch_size = 64, learning_rate_m = 1e-7, learning_rate_b = 1e-1). Then linearly increase the batch size and learning rate until you see the training does not converge. \n",
    "```\n",
    "(64, 1e-7, 1e-1)*4\n",
    "(64, 1e-7, 1e-1)*16\n",
    "(64, 1e-7, 1e-1)*32\n",
    "...\n",
    "```\n",
    "\n",
    "**How to submit your homework**\n",
    "* Fork the github repo to your personal github \n",
    "* Make change to the 01_linear_regression_sgd.ipynb, and then push to your personal github\n",
    "* Provide the link of 01_linear_regression_sgd in the personal github. \n",
    "\n",
    "Follow the below instruction on how to do this: \n",
    "https://github.com/argonne-lcf/ai-science-training-series/blob/main/00_introToAlcf/03_githubHomework.md"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "datascience/conda-2023-01-10",
   "language": "python",
   "name": "conda-2023-01-10"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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