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 during the lecture (use ```debug``` queue outside of the lecture)\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 learned English differently. She learns speaking by hearing a lot of speaking from TV, teachers, classmates, and her older brother. 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/llm2.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": 1,
   "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": 2,
   "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": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='GrLivArea'>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "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",
    "$$m = { n (\\Sigma xy) - (\\Sigma x) (\\Sigma y) \\over n (\\Sigma x^2) - (\\Sigma x)^2 } $$\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": 4,
   "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": 5,
   "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": 6,
   "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": 7,
   "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": 8,
   "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": 9,
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "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": 11,
   "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": 12,
   "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": 13,
   "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": 14,
   "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": 15,
   "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": 16,
   "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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",
      "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": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[029]  dy_i = 88.89 * x + 32912.24     previously calculated: y_i = 87.69 * x + 34754.08    loss: 1478200827.641291\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "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)//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)*1\n",
    "(64, 1e-7, 1e-1)*2\n",
    "(64, 1e-7, 1e-1)*4\n",
    "(64, 1e-7, 1e-1)*8\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": "markdown",
   "metadata": {},
   "source": [
    "# Homework answer\n",
    "\n",
    "Let us define a train function which allow us to try different hyperparameter setups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = data['GrLivArea'].to_numpy()\n",
    "y = data['SalePrice'].to_numpy()\n",
    "\n",
    "def train(batch_size, epochs=30, learning_rate_m = 1e-7, learning_rate_b = 1e-1):\n",
    "    loss_history = []\n",
    "    num_batches = len(data)//batch_size\n",
    "    loop_N = epochs*num_batches\n",
    "    m = 5.\n",
    "    b = 1000.\n",
    "    for i in range(loop_N):\n",
    "        data_batch = data.sample(batch_size)\n",
    "        data_x = data_batch['GrLivArea'].to_numpy()\n",
    "        data_y = data_batch['SalePrice'].to_numpy()\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",
    "    #loss_last_epoch = np.sum(loss_history[-num_batches:]*batch_size)/len(data)\n",
    "    return m, b, np.mean(loss(x,y,m,b))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Minibatch training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "previously calculated: y_i = 87.69 * x + 34754.08    loss: 1504269071.828533\n",
      "=======================================\n",
      "batch size: 64, m=86.6872, b=37479.4684, loss=1479789023.6492\n",
      "batch size: 128, m=89.0525, b=33751.2773, loss=1479135943.5381\n",
      "batch size: 256, m=88.4928, b=34082.7256, loss=1478172522.2247\n",
      "batch size: 512, m=89.1933, b=32665.9375, loss=1478404851.1370\n"
     ]
    }
   ],
   "source": [
    "print('previously calculated: y_i = %.2f * x + %.2f    loss: %f\\n=======================================' % (m_calc,b_calc,loss_value))\n",
    "\n",
    "\n",
    "for bs in 64, 128, 256, 512:\n",
    "    m, b, l = train(bs, epochs=30)\n",
    "    print(f\"batch size: {bs}, m={m:.4f}, b={b:.4f}, loss={l:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that eventually, we all get similar results with the minibatch training. Of course, here, we still keep the same learning rate. A gene"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "batch size: 64, m=91.2509, b=31854.0306, loss=1485746610.5624\n",
      "batch size: 128, m=80.6417, b=36734.1681, loss=1554481490.3060\n",
      "batch size: 256, m=93.8261, b=28853.2241, loss=1495644038.5204\n",
      "batch size: 512, m=48427.2742, b=68103516.7542, loss=19173027234859892.0000\n"
     ]
    }
   ],
   "source": [
    "for i in 1, 2, 4, 8:\n",
    "    bs, lrm, lrb = np.array([64, 1e-7, 1e-1])*i\n",
    "    bs = int(bs)\n",
    "    m, b, l = train(int(bs), epochs=30, learning_rate_m = lrm, learning_rate_b = lrb)\n",
    "    print(f\"batch size: {bs}, m={m:.4f}, b={b:.4f}, loss={l:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that, if we increase the batch size and the learning rate proportionally, at certain point, it does not converge for example for the case batch size = 512. To increase the learning rate proportional to the batch size is a general practice. However, if the learning rate is too large, it will continue to move around without finding a local minimum. One trick, people can do is to start with a smaller learning rate in the first few steps / epochs, and once the optimization becomes stable, increase the learning rate proportional to the batch size. "
   ]
  }
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