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  {
   "cell_type": "markdown",
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   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Learning\n",
    "\n",
    "This notebook serves as supporting material for topics covered in **Chapter 18 - Learning from Examples** , **Chapter 19 - Knowledge in Learning**, **Chapter 20 - Learning Probabilistic Models** from the book *Artificial Intelligence: A Modern Approach*. This notebook uses implementations from [learning.py](https://github.com/aimacode/aima-python/blob/master/learning.py). Let's start by importing everything from learning module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
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   "source": [
    "from learning import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Review\n",
    "\n",
    "In this notebook, we learn about agents that can improve their behavior through diligent study of their own experiences.\n",
    "\n",
    "An agent is **learning** if it improves its performance on future tasks after making observations about the world.\n",
    "\n",
    "There are three types of feedback that determine the three main types of learning:\n",
    "\n",
    "* **Supervised Learning**:\n",
    "\n",
    "In Supervised Learning the agent observeses some example input-output pairs and learns a function that maps from input to output.\n",
    "\n",
    "**Example**: Let's think of an agent to classify images containing cats or dogs. If we provide an image containing a cat or a dog, this agent should output a string \"cat\" or \"dog\" for that particular image. To teach this agent, we will give a lot of input-output pairs like {cat image-\"cat\"}, {dog image-\"dog\"} to the aggent. The agent then learns a function that maps from an input image to one of those strings.\n",
    "\n",
    "* **Unsupervised Learning**:\n",
    "\n",
    "In Unsupervised Learning the agent learns patterns in the input even though no explicit feedback is supplied. The most common type is **clustering**: detecting potential useful clusters of input examples.\n",
    "\n",
    "**Example**: A taxi agent would develop a concept of *good traffic days* and *bad traffic days* without ever being given labeled examples.\n",
    "\n",
    "* **Reinforcement Learning**:\n",
    "\n",
    "In Reinforcement Learning the agent from a series of reinforcements—rewards or punishments.\n",
    "\n",
    "**Example**: Let's talk about an agent to play the popular Atari game—[Pong](http://www.ponggame.org). We will reward a point for every correct move and deduct a point for every wrong move from the agent. Eventually, the agent will figure out its actions prior to reinforcement were most responsible for it."
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Explanations of learning module goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Practical Machine Learning Task\n",
    "## MNIST handwritten digits calssification\n",
    "\n",
    "The MNIST database, available from [this page](http://yann.lecun.com/exdb/mnist/) is a large database of handwritten digits that is commonly used for training & testing/validating in Machine learning.\n",
    "\n",
    "The dataset has **60,000 training images** each of size 28x28 pixels with labels and **10,000 testing images** of size 28x28 pixels with labels.\n",
    "\n",
    "In this section, we will use this database to compare performances of these different learning algorithms:\n",
    "* kNN (k-Nearest Neighbour) classifier\n",
    "* Single-hidden-layer Neural Network classifier\n",
    "* SVMs (Support Vector Machines)\n",
    "\n",
    "It is estimates that humans have an error rate of about **0.2%** on this problem. Let's see how our algorithms perform!\n",
    "\n",
    "Let's start by loading MNIST data into numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, struct\n",
    "import array\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_MNIST(path=\"aima-data/MNIST\"):\n",
    "    \"helper function to load MNIST data\"\n",
    "    train_img_file = open(os.path.join(path, \"train-images-idx3-ubyte\"), \"rb\")\n",
    "    train_lbl_file = open(os.path.join(path, \"train-labels-idx1-ubyte\"), \"rb\")\n",
    "    test_img_file = open(os.path.join(path, \"t10k-images-idx3-ubyte\"), \"rb\")\n",
    "    test_lbl_file = open(os.path.join(path, 't10k-labels-idx1-ubyte'), \"rb\")\n",
    "    \n",
    "    magic_nr, tr_size, tr_rows, tr_cols = struct.unpack(\">IIII\", train_img_file.read(16))\n",
    "    tr_img = array.array(\"B\", train_img_file.read())\n",
    "    train_img_file.close()    \n",
    "    magic_nr, tr_size = struct.unpack(\">II\", train_lbl_file.read(8))\n",
    "    tr_lbl = array.array(\"b\", train_lbl_file.read())\n",
    "    train_lbl_file.close()\n",
    "    \n",
    "    magic_nr, te_size, te_rows, te_cols = struct.unpack(\">IIII\", test_img_file.read(16))\n",
    "    te_img = array.array(\"B\", test_img_file.read())\n",
    "    test_img_file.close()\n",
    "    magic_nr, te_size = struct.unpack(\">II\", test_lbl_file.read(8))\n",
    "    te_lbl = array.array(\"b\", test_lbl_file.read())\n",
    "    test_lbl_file.close()\n",
    "\n",
    "#     print(len(tr_img), len(tr_lbl), tr_size)\n",
    "#     print(len(te_img), len(te_lbl), te_size)\n",
    "    \n",
    "    train_img = np.zeros((tr_size, tr_rows*tr_cols), dtype=np.uint8)\n",
    "    train_lbl = np.zeros((tr_size,), dtype=np.int8)\n",
    "    for i in range(tr_size):\n",
    "        train_img[i] = np.array(tr_img[i*tr_rows*tr_cols : (i+1)*tr_rows*tr_cols]).reshape((tr_rows*te_cols))\n",
    "        train_lbl[i] = tr_lbl[i]\n",
    "        \n",
    "    test_img = np.zeros((te_size, te_rows*te_cols), dtype=np.uint8)\n",
    "    test_lbl = np.zeros((te_size,), dtype=np.int8)\n",
    "    for i in range(te_size):\n",
    "        test_img[i] = np.array(te_img[i*te_rows*te_cols : (i+1)*te_rows*te_cols]).reshape((te_rows*te_cols))\n",
    "        test_lbl[i] = te_lbl[i]\n",
    "        \n",
    "    return(train_img, train_lbl, test_img, test_lbl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `load_MNIST()` loads MNIST data from files saved in `aima-data/MNIST`. It returns four numpy arrays that we are gonna use to train & classify hand-written digits in various learning approaches."
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "train_img, train_lbl, test_img, test_lbl = load_MNIST()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the shape of these NumPy arrays to make sure we have loaded the database correctly.\n",
    "\n",
    "Each 28x28 pixel image is flattened to 784x1 array and we should have 60,000 of them in training data. Similarly we should have 10,000 of those 784x1 arrays in testing data. "
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training images size: (60000, 784)\n",
      "Training labels size: (60000,)\n",
      "Testing images size: (10000, 784)\n",
      "Training labels size: (10000,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Training images size:\", train_img.shape)\n",
    "print(\"Training labels size:\", train_lbl.shape)\n",
    "print(\"Testing images size:\", test_img.shape)\n",
    "print(\"Training labels size:\", test_lbl.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get a better understanding of the dataset, let's visualize some random images for each class from training & testing datasets."
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "classes = [\"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\"]\n",
    "num_classes = len(classes)\n",
    "\n",
    "def show_MNIST(dataset, samples=8):\n",
    "    if dataset == \"training\":\n",
    "        labels = train_lbl\n",
    "        images = train_img\n",
    "    elif dataset == \"testing\":\n",
    "        labels = test_lbl\n",
    "        images = test_img\n",
    "    else:\n",
    "        raise ValueError(\"dataset must be 'testing' or 'training'!\")\n",
    "        \n",
    "    for y, cls in enumerate(classes):\n",
    "        idxs = np.nonzero([i == y for i in labels])\n",
    "        idxs = np.random.choice(idxs[0], samples, replace=False)\n",
    "        for i , idx in enumerate(idxs):\n",
    "            plt_idx = i * num_classes + y + 1\n",
    "            plt.subplot(samples, num_classes, plt_idx)\n",
    "            plt.imshow(images[idx].reshape((28, 28)))\n",
    "            plt.axis(\"off\")\n",
    "            if i == 0:\n",
    "                plt.title(cls)\n",
    "\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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KhN9OZr179wacQfCPP/4IQPXq1fP0nPHsY6tWrQA44YQTAHjvvfcAmDNnDvXr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\n//jjj/aPP/5oN2vWzG7WrFm6+6Wt8l7NnTvXzp8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GqPvoj+zZs/PHH38Ador/U089ZdTG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\nSUVORK5CYII=\n",
       "<matplotlib.figure.Figure at 0x108bc9470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 secs. to execute the cell\n",
    "show_MNIST(\"training\")"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TQ1ajEvMNpEePHsaYrnXr1oDbGTzekWR3iB+VLJANGzaY3e4DDzwAZN50Twzr8ufPb8zP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\nqXxUEnil5DQcZJUuyk80c70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yVZ4URVEURVHCwDfKk+QISAl0oOokcei77roLCD+xceXK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z76CHBX4YPc2/r27WvsCMRywFt1Kl26NGCrMxUrVjTXWimuWrhwobEqiTViPbBlyxbznUpnhsKF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\nTJs2Lc6jU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       "<matplotlib.figure.Figure at 0x1155756d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 secs. to execute the cell\n",
    "show_MNIST(\"testing\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at average of all the images of training and testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "classes = [\"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\"]\n",
    "num_classes = len(classes)\n",
    "\n",
    "def show_ave_MNIST(dataset):\n",
    "    if dataset == \"training\":\n",
    "        print(\"Average of all images in training dataset.\")\n",
    "        labels = train_lbl\n",
    "        images = train_img\n",
    "    elif dataset == \"testing\":\n",
    "        print(\"Average of all images in testing dataset.\")\n",
    "        labels = test_lbl\n",
    "        images = test_img\n",
    "    else:\n",
    "        raise ValueError(\"dataset must be 'testing' or 'training'!\")\n",
    "        \n",
    "    for y, cls in enumerate(classes):\n",
    "        idxs = np.nonzero([i == y for i in labels])\n",
    "        print(\"Digit\", y, \":\", len(idxs[0]), \"images.\")\n",
    "        \n",
    "        ave_img = np.mean(np.vstack([images[i] for i in idxs[0]]), axis = 0)\n",
    "#         print(ave_img.shape)\n",
    "        \n",
    "        plt.subplot(1, num_classes, y+1)\n",
    "        plt.imshow(ave_img.reshape((28, 28)))\n",
    "        plt.axis(\"off\")\n",
    "        plt.title(cls)\n",
    "\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of all images in training dataset.\n",
      "Digit 0 : 5923 images.\n",
      "Digit 1 : 6742 images.\n",
      "Digit 2 : 5958 images.\n",
      "Digit 3 : 6131 images.\n",
      "Digit 4 : 5842 images.\n",
      "Digit 5 : 5421 images.\n",
      "Digit 6 : 5918 images.\n",
      "Digit 7 : 6265 images.\n",
      "Digit 8 : 5851 images.\n",
      "Digit 9 : 5949 images.\n"
     ]
    },
    {
     "data": {
      "image/png": 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HYy6YarXakv8GQMvWdK5EtfVEpen69esAmlvHp6amZKVLNWtlZUXcLeGZbN1C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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1142f1e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of all images in testing dataset.\n",
      "Digit 0 : 980 images.\n",
      "Digit 1 : 1135 images.\n",
      "Digit 2 : 1032 images.\n",
      "Digit 3 : 1010 images.\n",
      "Digit 4 : 982 images.\n",
      "Digit 5 : 892 images.\n",
      "Digit 6 : 958 images.\n",
      "Digit 7 : 1028 images.\n",
      "Digit 8 : 974 images.\n",
      "Digit 9 : 1009 images.\n"
     ]
    },
    {
     "data": {
      "image/png": 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SfjrinGO899LX2H+dc9I3aSPwOSwtLSVuu9q2nWEYhmEYRsYcCuWpu7tbvBgd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\nwzCMFjDjyTAMwzAMowX+P+71/Wk0f7yTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1146c7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_ave_MNIST(\"training\")\n",
    "show_ave_MNIST(\"testing\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k-Nearest Neighbours (kNN) classifier"
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  },
  "widgets": {
   "state": {},
   "version": "1.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}