NaiveBaiyes.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mxnet import nd, gluon\n",
    "import matplotlib.pyplot as plt\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "def transform(data, label):\n",
    "    return (data/128).astype('float32').squeeze(axis=-1), label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_images(imgs, rows, cols):\n",
    "    _, axes = plt.subplots(rows, cols)\n",
    "    axes = axes.flatten()\n",
    "    for ax, img in zip(axes, imgs):\n",
    "        ax.imshow(img.asnumpy())\n",
    "        ax.get_xaxis().set_visible(False)\n",
    "        ax.get_yaxis().set_visible(False)\n",
    "    plt.show()\n",
    "    return axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeYProbs(Y, n_classes):\n",
    "    n_y = nd.zeros(n_classes)\n",
    "    for i in range(n_classes):\n",
    "        n_y[i] = (Y==i).sum()\n",
    "    P_y = n_y / n_y.sum()\n",
    "    return P_y, n_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeXProbs(X, n_y, n_classes):\n",
    "    n_x = nd.zeros((n_classes, X.shape[1], X.shape[2]))\n",
    "    for i in range(n_classes):\n",
    "        n_x[i] = nd.array(X.asnumpy()[Y==i].sum(axis=0))\n",
    "    P_xy = (n_x+1) / (n_y+1).reshape((10, 1, 1))\n",
    "    return P_xy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(img, P_xy, P_y, n_classes):\n",
    "    img = img.expand_dims(axis=0)\n",
    "    log_P_xy = nd.log(P_xy)\n",
    "    log_neg_P_xy = nd.log(1-P_xy)\n",
    "    pxy = log_P_xy * img + log_neg_P_xy * (1-img)\n",
    "    pxy = pxy.reshape((n_classes, -1)).sum(axis=1)\n",
    "    probs = pxy + nd.log(P_y)\n",
    "    return probs.argmax(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "mnist_train = gluon.data.vision.datasets.MNIST(train=True, transform=transform)\n",
    "mnist_test = gluon.data.vision.datasets.MNIST(train=False, transform=transform)\n",
    "n_classes = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X shape (60000, 28, 28)\n",
      "Y shape (60000,)\n"
     ]
    }
   ],
   "source": [
    "X, Y = mnist_train[:]\n",
    "show_images(X, 2, 5)\n",
    "print('X shape', X.shape)\n",
    "print('Y shape', Y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10,)\n",
      "\n",
      "[0.09871667 0.11236667 0.0993     0.10218333 0.09736667 0.09035\n",
      " 0.09863333 0.10441667 0.09751666 0.09915   ]\n",
      "<NDArray 10 @cpu(0)>\n",
      "\n",
      "[1.]\n",
      "<NDArray 1 @cpu(0)>\n"
     ]
    }
   ],
   "source": [
    "P_y, n_y = computeYProbs(Y, n_classes)\n",
    "print(P_y.shape)\n",
    "print(P_y)\n",
    "print(P_y.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10, 28, 28)\n"
     ]
    }
   ],
   "source": [
    "P_xy = computeXProbs(X, n_y, n_classes)\n",
    "show_images(P_xy, 2, 5)\n",
    "print(P_xy.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "[1.]\n",
      "<NDArray 1 @cpu(0)>\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = X[random.randint(0, X.shape[0])]\n",
    "res = predict(test, P_xy, P_y, n_classes)\n",
    "print(res)\n",
    "plt.imshow(test.asnumpy())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}