mnist-mini-project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# MSAIL Tutorial Series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "## MNIST Mini-Project"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "So far we have covered 4 supervised [classfication](https://github.com/MSAIL/Curriculum/blob/master/classification.ipynb) algorithms:\n",
    "* Logistic Regression\n",
    "* Support Vector Machines (SVM)\n",
    "* k Nearest Neighbors (kNN)\n",
    "* Naive Bayes\n",
    "\n",
    "Now let us apply these to a larger dataset, namely [MNIST](http://yann.lecun.com/exdb/mnist/). In the process we will observe how we can adapt these algorithms for multi-class rather than binary classification."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import fetch_mldata\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "mnist = fetch_mldata('MNIST original', data_home='/Users/nanddalal/tmp/')\n",
    "\n",
    "x = mnist.data\n",
    "y = mnist.target\n",
    "xy = np.c_[x,y]\n",
    "np.random.shuffle(xy)\n",
    "\n",
    "train_x = xy[0:1000, 0:784]\n",
    "train_y = xy[0:1000, -1]\n",
    "test_x = xy[1000:1100, 0:784]\n",
    "test_y = xy[1000:1100, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def train_and_test(model, xtrain, ytrain, xtest, ytest):\n",
    "    model = model.fit(xtrain, ytrain)\n",
    "    output = model.predict(xtest)\n",
    "    print (1.0 * sum([i==j for (i, j) in zip(output, ytest)])) / len(ytest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.0\n"
     ]
    },
    {
     "data": {
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vI3zLifDHZnV3bXHO+04/7E45E/4p4YeE5f5bsoPuhVLqnwH/MfB3gP9BKfVv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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124378810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(train_x[1].reshape(28, 28))\n",
    "print train_y[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### k Nearest Neighbors (kNN)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.91\n"
     ]
    }
   ],
   "source": [
    "import sklearn.neighbors\n",
    "model = sklearn.neighbors.KNeighborsClassifier(3, weights='distance')\n",
    "train_and_test(model, train_x, train_y, test_x, test_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Naive Bayes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.81\n"
     ]
    }
   ],
   "source": [
    "import sklearn.naive_bayes\n",
    "model = sklearn.naive_bayes.MultinomialNB()\n",
    "train_and_test(model, train_x, train_y, test_x, test_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Logistic Regression -> Softmax Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.83\n"
     ]
    }
   ],
   "source": [
    "import sklearn.linear_model\n",
    "model = sklearn.linear_model.LogisticRegression()\n",
    "train_and_test(model, train_x, train_y, test_x, test_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Support Vector Machines (SVM)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.82\n",
      "0.08\n"
     ]
    }
   ],
   "source": [
    "import sklearn.svm\n",
    "model = sklearn.svm.LinearSVC()\n",
    "train_and_test(model, train_x, train_y, test_x, test_y)\n",
    "model = sklearn.svm.SVC(kernel=\"rbf\")\n",
    "train_and_test(model, train_x, train_y, test_x, test_y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<img src=\"https://upload.wikimedia.org/wikipedia/commons/4/46/Colored_neural_network.svg\" height=\"200\" width=\"200\">\n",
    "\n",
    "Let us quickly review [logistic regression](https://github.com/MSAIL/Curriculum/blob/master/classification.ipynb). Now we can think about neural networks as running several logistic regressions at the same time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "train_y_probs = np.zeros((1000, 10))\n",
    "for i in range(1000):\n",
    "    train_y_probs[i][int(train_y[i])] = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "class NeuralNetwork:\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.weights = np.random.randn(784,10)\n",
    "        self.biases = np.random.randn(10)\n",
    "    \n",
    "    def softmax(self, x):\n",
    "        e_x = np.exp(x - np.max(x))\n",
    "        out = e_x / e_x.sum()\n",
    "        return out\n",
    "\n",
    "    def fit(self, train_x, train_y):        \n",
    "        for it in range(300):\n",
    "            if it % 100 == 0:\n",
    "                print \"Epoch\", it\n",
    "\n",
    "            for i in range(1000):\n",
    "                # Forward propagation\n",
    "                input_layer = train_x[i]\n",
    "                hidden_layer = np.dot(input_layer, self.weights) + self.biases\n",
    "                output_layer = self.softmax(hidden_layer)\n",
    "\n",
    "                # Back propagation\n",
    "                \n",
    "                grad = output_layer - train_y[i]\n",
    "\n",
    "                w_grad_hid = np.dot(input_layer.reshape(784,1), grad.reshape(1,10))\n",
    "                b_grad_hid = w_grad_hid.sum(axis=0)\n",
    "\n",
    "                self.weights -= w_grad_hid\n",
    "                self.biases -= b_grad_hid\n",
    "        \n",
    "        return self\n",
    "\n",
    "    def predict(self, test_x):\n",
    "        preds = np.zeros(100)\n",
    "        for i in range(100):\n",
    "            pred = self.softmax(np.dot(test_x[i], self.weights) + self.biases)\n",
    "            preds[i] = np.argmax(pred)\n",
    "        return preds\n",
    "    \n",
    "    def visualize(self):\n",
    "        for i in range(10):\n",
    "            plt.subplot(1, 10, i+1)\n",
    "            plt.axis('off')\n",
    "            plt.set_cmap('gray')\n",
    "            plt.imshow(model.weights[:,i].reshape(28, 28))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0\n",
      "Epoch 100\n",
      "Epoch 200\n",
      "0.82\n"
     ]
    }
   ],
   "source": [
    "model = NeuralNetwork()\n",
    "train_and_test(model, train_x, train_y_probs, test_x, test_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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XC16vlyN44IXhFEURPp8PkiSh3+9DEAQMBgN0u12srq4iEAhAEATIsgy32410Og3gRZYy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\nWygUsLKywgMK9DouoqnNiy8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x12476b0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.visualize()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}