170904_p83.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 3 Clasification (p.83)\n",
    "## Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# To support both python 2 and python 3\n",
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "# Where to save the figures\n",
    "PROJECT_ROOT_DIR = \".\"\n",
    "CHAPTER_ID = \"classification\"\n",
    "\n",
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, \"images\", CHAPTER_ID, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def save_fig(fig_id, tight_layout=True):\n",
    "    path = os.path.join(PROJECT_ROOT_DIR, fig_id + \".png\")\n",
    "    print(\"Saving figure\", fig_id)\n",
    "    if tight_layout:\n",
    "        plt.tight_layout()\n",
    "    plt.savefig(path, format='png', dpi=300)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### pip install keras (事前にインストールしておく)\n",
    "### pip install tensorflow (こちらも要るかも？)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST (p.83)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from keras.datasets import mnist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<module 'keras.datasets.mnist' from 'C:\\\\ProgramData\\\\Anaconda3\\\\lib\\\\site-packages\\\\keras\\\\datasets\\\\mnist.py'>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(X_train,y_train),(X_test,y_test)=mnist.load_data()\n",
    "X_train=X_train.reshape(60000,784)/255\n",
    "X_test=X_test.reshape(10000,784)/255"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 784)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000,)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 784)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "28*28"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "plt.style.use('ggplot')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number:9\n"
     ]
    }
   ],
   "source": [
    "#some_digit = X[36000] in book\n",
    "idx=36000\n",
    "size=28\n",
    "a,b=np.meshgrid(range(size),range(size))\n",
    "some_digit_image=X_train[idx].reshape(size,size)\n",
    "some_digit_image=some_digit_image[::-1,:]\n",
    "print('number:{}'.format(y_train[idx]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure some_digit_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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0adMs2//whz9YzvP73/8+ZP8vfvELyzkOHTpkOea73/3umO20tDS9/PLLge3S0lLLOZ5k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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x284e21e9f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x284e026c160>"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAALMAAACtCAYAAAD7yE4YAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x284e1f65cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(some_digit_image, cmap = matplotlib.cm.binary,\n",
    "           interpolation=\"nearest\")\n",
    "#plt.axis(\"off\")\n",
    "save_fig(\"some_digit_plot\")\n",
    "plt.show()\n",
    "\n",
    "plt.figure(figsize=(2.5,2.5))\n",
    "plt.xlim(0,27)\n",
    "plt.ylim(0,27)\n",
    "plt.pcolor(a,b,some_digit_image)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[36000]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_digits(instances, images_per_row=10, **options):\n",
    "    size = 28\n",
    "    images_per_row = min(len(instances), images_per_row)\n",
    "    images = [instance.reshape(size,size) for instance in instances]\n",
    "    n_rows = (len(instances) - 1) // images_per_row + 1\n",
    "    row_images = []\n",
    "    n_empty = n_rows * images_per_row - len(instances)\n",
    "    images.append(np.zeros((size, size * n_empty)))\n",
    "    for row in range(n_rows):\n",
    "        rimages = images[row * images_per_row : (row + 1) * images_per_row]\n",
    "        row_images.append(np.concatenate(rimages, axis=1))\n",
    "    image = np.concatenate(row_images, axis=0)\n",
    "    plt.imshow(image, cmap = matplotlib.cm.binary, **options)\n",
    "    plt.axis(\"off\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure more_digits_plot\n"
     ]
    },
    {
     "data": {
      "image/png": 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+O/FomnaH1CJII/uy/Hj1XFZOnXYM3nrrLSBEyuLU/ibZIiyLFP1TqyKNBlWt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\nUnleYf18/PHHAGy11VbReZ9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TOGqnoYauNVl22WULvRwgRO/0N3juuecA2GWXXaLrKFH7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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x284e1f0eef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(9,9))\n",
    "example_images = np.r_[X_train[:12000:600], X_train[13000:30600:600], X_train[30600:60000:590]]\n",
    "plot_digits(example_images, images_per_row=10)\n",
    "save_fig(\"more_digits_plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "training dataは数字が順番に並んでいるので、cross validationする時の分割用に\n",
    "シャッフルしておく"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "shuffle_index = np.random.permutation(60000)\n",
    "X_train, y_train = X_train[shuffle_index], y_train[shuffle_index]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training a binary classifier(p.87)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "手書き画像5データのみ抽出。5か5でないかの分類器を作成する。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train_5 = (y_train == 5)\n",
    "y_test_5 = (y_test == 5)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "確率的勾配降下法(Stochastic Gradient Descent classifier)を使う\n",
    "https://ja.wikipedia.org/wiki/%E7%A2%BA%E7%8E%87%E7%9A%84%E5%8B%BE%E9%85%8D%E9%99%8D%E4%B8%8B%E6%B3%95"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SGDClassifier(alpha=0.0001, average=False, class_weight=None, epsilon=0.1,\n",
       "       eta0=0.0, fit_intercept=True, l1_ratio=0.15,\n",
       "       learning_rate='optimal', loss='hinge', n_iter=5, n_jobs=1,\n",
       "       penalty='l2', power_t=0.5, random_state=42, shuffle=True, verbose=0,\n",
       "       warm_start=False)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDClassifier\n",
    "\n",
    "sgd_clf = SGDClassifier(random_state=42)\n",
    "sgd_clf.fit(X_train, y_train_5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class SGDClassifier in module sklearn.linear_model.stochastic_gradient:\n",
      "\n",
      "class SGDClassifier(BaseSGDClassifier, sklearn.feature_selection.from_model._LearntSelectorMixin)\n",
      " |  Linear classifiers (SVM, logistic regression, a.o.) with SGD training.\n",
      " |  \n",
      " |  This estimator implements regularized linear models with stochastic\n",
      " |  gradient descent (SGD) learning: the gradient of the loss is estimated\n",
      " |  each sample at a time and the model is updated along the way with a\n",
      " |  decreasing strength schedule (aka learning rate). SGD allows minibatch\n",
      " |  (online/out-of-core) learning, see the partial_fit method.\n",
      " |  For best results using the default learning rate schedule, the data should\n",
      " |  have zero mean and unit variance.\n",
      " |  \n",
      " |  This implementation works with data represented as dense or sparse arrays\n",
      " |  of floating point values for the features. The model it fits can be\n",
      " |  controlled with the loss parameter; by default, it fits a linear support\n",
      " |  vector machine (SVM).\n",
      " |  \n",
      " |  The regularizer is a penalty added to the loss function that shrinks model\n",
      " |  parameters towards the zero vector using either the squared euclidean norm\n",
      " |  L2 or the absolute norm L1 or a combination of both (Elastic Net). If the\n",
      " |  parameter update crosses the 0.0 value because of the regularizer, the\n",
      " |  update is truncated to 0.0 to allow for learning sparse models and achieve\n",
      " |  online feature selection.\n",
      " |  \n",
      " |  Read more in the :ref:`User Guide <sgd>`.\n",
      " |  \n",
      " |  Parameters\n",
      " |  ----------\n",
      " |  loss : str, 'hinge', 'log', 'modified_huber', 'squared_hinge',                'perceptron', or a regression loss: 'squared_loss', 'huber',                'epsilon_insensitive', or 'squared_epsilon_insensitive'\n",
      " |      The loss function to be used. Defaults to 'hinge', which gives a\n",
      " |      linear SVM.\n",
      " |      The 'log' loss gives logistic regression, a probabilistic classifier.\n",
      " |      'modified_huber' is another smooth loss that brings tolerance to\n",
      " |      outliers as well as probability estimates.\n",
      " |      'squared_hinge' is like hinge but is quadratically penalized.\n",
      " |      'perceptron' is the linear loss used by the perceptron algorithm.\n",
      " |      The other losses are designed for regression but can be useful in\n",
      " |      classification as well; see SGDRegressor for a description.\n",
      " |  \n",
      " |  penalty : str, 'none', 'l2', 'l1', or 'elasticnet'\n",
      " |      The penalty (aka regularization term) to be used. Defaults to 'l2'\n",
      " |      which is the standard regularizer for linear SVM models. 'l1' and\n",
      " |      'elasticnet' might bring sparsity to the model (feature selection)\n",
      " |      not achievable with 'l2'.\n",
      " |  \n",
      " |  alpha : float\n",
      " |      Constant that multiplies the regularization term. Defaults to 0.0001\n",
      " |      Also used to compute learning_rate when set to 'optimal'.\n",
      " |  \n",
      " |  l1_ratio : float\n",
      " |      The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1.\n",
      " |      l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1.\n",
      " |      Defaults to 0.15.\n",
      " |  \n",
      " |  fit_intercept : bool\n",
      " |      Whether the intercept should be estimated or not. If False, the\n",
      " |      data is assumed to be already centered. Defaults to True.\n",
      " |  \n",
      " |  n_iter : int, optional\n",
      " |      The number of passes over the training data (aka epochs). The number\n",
      " |      of iterations is set to 1 if using partial_fit.\n",
      " |      Defaults to 5.\n",
      " |  \n",
      " |  shuffle : bool, optional\n",
      " |      Whether or not the training data should be shuffled after each epoch.\n",
      " |      Defaults to True.\n",
      " |  \n",
      " |  random_state : int seed, RandomState instance, or None (default)\n",
      " |      The seed of the pseudo random number generator to use when\n",
      " |      shuffling the data.\n",
      " |  \n",
      " |  verbose : integer, optional\n",
      " |      The verbosity level\n",
      " |  \n",
      " |  epsilon : float\n",
      " |      Epsilon in the epsilon-insensitive loss functions; only if `loss` is\n",
      " |      'huber', 'epsilon_insensitive', or 'squared_epsilon_insensitive'.\n",
      " |      For 'huber', determines the threshold at which it becomes less\n",
      " |      important to get the prediction exactly right.\n",
      " |      For epsilon-insensitive, any differences between the current prediction\n",
      " |      and the correct label are ignored if they are less than this threshold.\n",
      " |  \n",
      " |  n_jobs : integer, optional\n",
      " |      The number of CPUs to use to do the OVA (One Versus All, for\n",
      " |      multi-class problems) computation. -1 means 'all CPUs'. Defaults\n",
      " |      to 1.\n",
      " |  \n",
      " |  learning_rate : string, optional\n",
      " |      The learning rate schedule:\n",
      " |  \n",
      " |      - 'constant': eta = eta0\n",
      " |      - 'optimal': eta = 1.0 / (alpha * (t + t0)) [default]\n",
      " |      - 'invscaling': eta = eta0 / pow(t, power_t)\n",
      " |  \n",
      " |      where t0 is chosen by a heuristic proposed by Leon Bottou.\n",
      " |  \n",
      " |  eta0 : double\n",
      " |      The initial learning rate for the 'constant' or 'invscaling'\n",
      " |      schedules. The default value is 0.0 as eta0 is not used by the\n",
      " |      default schedule 'optimal'.\n",
      " |  \n",
      " |  power_t : double\n",
      " |      The exponent for inverse scaling learning rate [default 0.5].\n",
      " |  \n",
      " |  class_weight : dict, {class_label: weight} or \"balanced\" or None, optional\n",
      " |      Preset for the class_weight fit parameter.\n",
      " |  \n",
      " |      Weights associated with classes. If not given, all classes\n",
      " |      are supposed to have weight one.\n",
      " |  \n",
      " |      The \"balanced\" mode uses the values of y to automatically adjust\n",
      " |      weights inversely proportional to class frequencies in the input data\n",
      " |      as ``n_samples / (n_classes * np.bincount(y))``\n",
      " |  \n",
      " |  warm_start : bool, optional\n",
      " |      When set to True, reuse the solution of the previous call to fit as\n",
      " |      initialization, otherwise, just erase the previous solution.\n",
      " |  \n",
      " |  average : bool or int, optional\n",
      " |      When set to True, computes the averaged SGD weights and stores the\n",
      " |      result in the ``coef_`` attribute. If set to an int greater than 1,\n",
      " |      averaging will begin once the total number of samples seen reaches\n",
      " |      average. So ``average=10`` will begin averaging after seeing 10\n",
      " |      samples.\n",
      " |  \n",
      " |  Attributes\n",
      " |  ----------\n",
      " |  coef_ : array, shape (1, n_features) if n_classes == 2 else (n_classes,            n_features)\n",
      " |      Weights assigned to the features.\n",
      " |  \n",
      " |  intercept_ : array, shape (1,) if n_classes == 2 else (n_classes,)\n",
      " |      Constants in decision function.\n",
      " |  \n",
      " |  Examples\n",
      " |  --------\n",
      " |  >>> import numpy as np\n",
      " |  >>> from sklearn import linear_model\n",
      " |  >>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])\n",
      " |  >>> Y = np.array([1, 1, 2, 2])\n",
      " |  >>> clf = linear_model.SGDClassifier()\n",
      " |  >>> clf.fit(X, Y)\n",
      " |  ... #doctest: +NORMALIZE_WHITESPACE\n",
      " |  SGDClassifier(alpha=0.0001, average=False, class_weight=None, epsilon=0.1,\n",
      " |          eta0=0.0, fit_intercept=True, l1_ratio=0.15,\n",
      " |          learning_rate='optimal', loss='hinge', n_iter=5, n_jobs=1,\n",
      " |          penalty='l2', power_t=0.5, random_state=None, shuffle=True,\n",
      " |          verbose=0, warm_start=False)\n",
      " |  >>> print(clf.predict([[-0.8, -1]]))\n",
      " |  [1]\n",
      " |  \n",
      " |  See also\n",
      " |  --------\n",
      " |  LinearSVC, LogisticRegression, Perceptron\n",
      " |  \n",
      " |  Method resolution order:\n",
      " |      SGDClassifier\n",
      " |      BaseSGDClassifier\n",
      " |      abc.NewBase\n",
      " |      BaseSGD\n",
      " |      abc.NewBase\n",
      " |      sklearn.base.BaseEstimator\n",
      " |      sklearn.linear_model.base.SparseCoefMixin\n",
      " |      sklearn.linear_model.base.LinearClassifierMixin\n",
      " |      sklearn.base.ClassifierMixin\n",
      " |      sklearn.feature_selection.from_model._LearntSelectorMixin\n",
      " |      sklearn.base.TransformerMixin\n",
      " |      builtins.object\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __init__(self, loss='hinge', penalty='l2', alpha=0.0001, l1_ratio=0.15, fit_intercept=True, n_iter=5, shuffle=True, verbose=0, epsilon=0.1, n_jobs=1, random_state=None, learning_rate='optimal', eta0=0.0, power_t=0.5, class_weight=None, warm_start=False, average=False)\n",
      " |      Initialize self.  See help(type(self)) for accurate signature.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors defined here:\n",
      " |  \n",
      " |  predict_log_proba\n",
      " |      Log of probability estimates.\n",
      " |      \n",
      " |      This method is only available for log loss and modified Huber loss.\n",
      " |      \n",
      " |      When loss=\"modified_huber\", probability estimates may be hard zeros\n",
      " |      and ones, so taking the logarithm is not possible.\n",
      " |      \n",
      " |      See ``predict_proba`` for details.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like, shape (n_samples, n_features)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      T : array-like, shape (n_samples, n_classes)\n",
      " |          Returns the log-probability of the sample for each class in the\n",
      " |          model, where classes are ordered as they are in\n",
      " |          `self.classes_`.\n",
      " |  \n",
      " |  predict_proba\n",
      " |      Probability estimates.\n",
      " |      \n",
      " |      This method is only available for log loss and modified Huber loss.\n",
      " |      \n",
      " |      Multiclass probability estimates are derived from binary (one-vs.-rest)\n",
      " |      estimates by simple normalization, as recommended by Zadrozny and\n",
      " |      Elkan.\n",
      " |      \n",
      " |      Binary probability estimates for loss=\"modified_huber\" are given by\n",
      " |      (clip(decision_function(X), -1, 1) + 1) / 2. For other loss functions\n",
      " |      it is necessary to perform proper probability calibration by wrapping\n",
      " |      the classifier with\n",
      " |      :class:`sklearn.calibration.CalibratedClassifierCV` instead.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      array, shape (n_samples, n_classes)\n",
      " |          Returns the probability of the sample for each class in the model,\n",
      " |          where classes are ordered as they are in `self.classes_`.\n",
      " |      \n",
      " |      References\n",
      " |      ----------\n",
      " |      Zadrozny and Elkan, \"Transforming classifier scores into multiclass\n",
      " |      probability estimates\", SIGKDD'02,\n",
      " |      http://www.research.ibm.com/people/z/zadrozny/kdd2002-Transf.pdf\n",
      " |      \n",
      " |      The justification for the formula in the loss=\"modified_huber\"\n",
      " |      case is in the appendix B in:\n",
      " |      http://jmlr.csail.mit.edu/papers/volume2/zhang02c/zhang02c.pdf\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data and other attributes defined here:\n",
      " |  \n",
      " |  __abstractmethods__ = frozenset()\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from BaseSGDClassifier:\n",
      " |  \n",
      " |  fit(self, X, y, coef_init=None, intercept_init=None, sample_weight=None)\n",
      " |      Fit linear model with Stochastic Gradient Descent.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
      " |          Training data\n",
      " |      \n",
      " |      y : numpy array, shape (n_samples,)\n",
      " |          Target values\n",
      " |      \n",
      " |      coef_init : array, shape (n_classes, n_features)\n",
      " |          The initial coefficients to warm-start the optimization.\n",
      " |      \n",
      " |      intercept_init : array, shape (n_classes,)\n",
      " |          The initial intercept to warm-start the optimization.\n",
      " |      \n",
      " |      sample_weight : array-like, shape (n_samples,), optional\n",
      " |          Weights applied to individual samples.\n",
      " |          If not provided, uniform weights are assumed. These weights will\n",
      " |          be multiplied with class_weight (passed through the\n",
      " |          constructor) if class_weight is specified\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self : returns an instance of self.\n",
      " |  \n",
      " |  partial_fit(self, X, y, classes=None, sample_weight=None)\n",
      " |      Fit linear model with Stochastic Gradient Descent.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape (n_samples, n_features)\n",
      " |          Subset of the training data\n",
      " |      \n",
      " |      y : numpy array, shape (n_samples,)\n",
      " |          Subset of the target values\n",
      " |      \n",
      " |      classes : array, shape (n_classes,)\n",
      " |          Classes across all calls to partial_fit.\n",
      " |          Can be obtained by via `np.unique(y_all)`, where y_all is the\n",
      " |          target vector of the entire dataset.\n",
      " |          This argument is required for the first call to partial_fit\n",
      " |          and can be omitted in the subsequent calls.\n",
      " |          Note that y doesn't need to contain all labels in `classes`.\n",
      " |      \n",
      " |      sample_weight : array-like, shape (n_samples,), optional\n",
      " |          Weights applied to individual samples.\n",
      " |          If not provided, uniform weights are assumed.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self : returns an instance of self.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data and other attributes inherited from BaseSGDClassifier:\n",
      " |  \n",
      " |  loss_functions = {'epsilon_insensitive': (<class 'sklearn.linear_model...\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from BaseSGD:\n",
      " |  \n",
      " |  set_params(self, *args, **kwargs)\n",
      " |      Set the parameters of this estimator.\n",
      " |      \n",
      " |      The method works on simple estimators as well as on nested objects\n",
      " |      (such as pipelines). The latter have parameters of the form\n",
      " |      ``<component>__<parameter>`` so that it's possible to update each\n",
      " |      component of a nested object.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.base.BaseEstimator:\n",
      " |  \n",
      " |  __getstate__(self)\n",
      " |  \n",
      " |  __repr__(self)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  __setstate__(self, state)\n",
      " |  \n",
      " |  get_params(self, deep=True)\n",
      " |      Get parameters for this estimator.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      deep : boolean, optional\n",
      " |          If True, will return the parameters for this estimator and\n",
      " |          contained subobjects that are estimators.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      params : mapping of string to any\n",
      " |          Parameter names mapped to their values.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors inherited from sklearn.base.BaseEstimator:\n",
      " |  \n",
      " |  __dict__\n",
      " |      dictionary for instance variables (if defined)\n",
      " |  \n",
      " |  __weakref__\n",
      " |      list of weak references to the object (if defined)\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.linear_model.base.SparseCoefMixin:\n",
      " |  \n",
      " |  densify(self)\n",
      " |      Convert coefficient matrix to dense array format.\n",
      " |      \n",
      " |      Converts the ``coef_`` member (back) to a numpy.ndarray. This is the\n",
      " |      default format of ``coef_`` and is required for fitting, so calling\n",
      " |      this method is only required on models that have previously been\n",
      " |      sparsified; otherwise, it is a no-op.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self: estimator\n",
      " |  \n",
      " |  sparsify(self)\n",
      " |      Convert coefficient matrix to sparse format.\n",
      " |      \n",
      " |      Converts the ``coef_`` member to a scipy.sparse matrix, which for\n",
      " |      L1-regularized models can be much more memory- and storage-efficient\n",
      " |      than the usual numpy.ndarray representation.\n",
      " |      \n",
      " |      The ``intercept_`` member is not converted.\n",
      " |      \n",
      " |      Notes\n",
      " |      -----\n",
      " |      For non-sparse models, i.e. when there are not many zeros in ``coef_``,\n",
      " |      this may actually *increase* memory usage, so use this method with\n",
      " |      care. A rule of thumb is that the number of zero elements, which can\n",
      " |      be computed with ``(coef_ == 0).sum()``, must be more than 50% for this\n",
      " |      to provide significant benefits.\n",
      " |      \n",
      " |      After calling this method, further fitting with the partial_fit\n",
      " |      method (if any) will not work until you call densify.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      self: estimator\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.linear_model.base.LinearClassifierMixin:\n",
      " |  \n",
      " |  decision_function(self, X)\n",
      " |      Predict confidence scores for samples.\n",
      " |      \n",
      " |      The confidence score for a sample is the signed distance of that\n",
      " |      sample to the hyperplane.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape = (n_samples, n_features)\n",
      " |          Samples.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      array, shape=(n_samples,) if n_classes == 2 else (n_samples, n_classes)\n",
      " |          Confidence scores per (sample, class) combination. In the binary\n",
      " |          case, confidence score for self.classes_[1] where >0 means this\n",
      " |          class would be predicted.\n",
      " |  \n",
      " |  predict(self, X)\n",
      " |      Predict class labels for samples in X.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : {array-like, sparse matrix}, shape = [n_samples, n_features]\n",
      " |          Samples.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      C : array, shape = [n_samples]\n",
      " |          Predicted class label per sample.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.base.ClassifierMixin:\n",
      " |  \n",
      " |  score(self, X, y, sample_weight=None)\n",
      " |      Returns the mean accuracy on the given test data and labels.\n",
      " |      \n",
      " |      In multi-label classification, this is the subset accuracy\n",
      " |      which is a harsh metric since you require for each sample that\n",
      " |      each label set be correctly predicted.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : array-like, shape = (n_samples, n_features)\n",
      " |          Test samples.\n",
      " |      \n",
      " |      y : array-like, shape = (n_samples) or (n_samples, n_outputs)\n",
      " |          True labels for X.\n",
      " |      \n",
      " |      sample_weight : array-like, shape = [n_samples], optional\n",
      " |          Sample weights.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      score : float\n",
      " |          Mean accuracy of self.predict(X) wrt. y.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.feature_selection.from_model._LearntSelectorMixin:\n",
      " |  \n",
      " |  transform(*args, **kwargs)\n",
      " |      DEPRECATED: Support to use estimators as feature selectors will be removed in version 0.19. Use SelectFromModel instead.\n",
      " |      \n",
      " |      Reduce X to its most important features.\n",
      " |      \n",
      " |              Uses ``coef_`` or ``feature_importances_`` to determine the most\n",
      " |              important features.  For models with a ``coef_`` for each class, the\n",
      " |              absolute sum over the classes is used.\n",
      " |      \n",
      " |              Parameters\n",
      " |              ----------\n",
      " |              X : array or scipy sparse matrix of shape [n_samples, n_features]\n",
      " |                  The input samples.\n",
      " |      \n",
      " |              threshold : string, float or None, optional (default=None)\n",
      " |                  The threshold value to use for feature selection. Features whose\n",
      " |                  importance is greater or equal are kept while the others are\n",
      " |                  discarded. If \"median\" (resp. \"mean\"), then the threshold value is\n",
      " |                  the median (resp. the mean) of the feature importances. A scaling\n",
      " |                  factor (e.g., \"1.25*mean\") may also be used. If None and if\n",
      " |                  available, the object attribute ``threshold`` is used. Otherwise,\n",
      " |                  \"mean\" is used by default.\n",
      " |      \n",
      " |              Returns\n",
      " |              -------\n",
      " |              X_r : array of shape [n_samples, n_selected_features]\n",
      " |                  The input samples with only the selected features.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Methods inherited from sklearn.base.TransformerMixin:\n",
      " |  \n",
      " |  fit_transform(self, X, y=None, **fit_params)\n",
      " |      Fit to data, then transform it.\n",
      " |      \n",
      " |      Fits transformer to X and y with optional parameters fit_params\n",
      " |      and returns a transformed version of X.\n",
      " |      \n",
      " |      Parameters\n",
      " |      ----------\n",
      " |      X : numpy array of shape [n_samples, n_features]\n",
      " |          Training set.\n",
      " |      \n",
      " |      y : numpy array of shape [n_samples]\n",
      " |          Target values.\n",
      " |      \n",
      " |      Returns\n",
      " |      -------\n",
      " |      X_new : numpy array of shape [n_samples, n_features_new]\n",
      " |          Transformed array.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(SGDClassifier)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MNIST X_train[36000]=\"9\"だったので手書き5画像モデルの予測値はFalseとなった"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([False], dtype=bool)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sgd_clf.predict([X_train[36000]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance measures (p.88)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "cross validationで手書き5予測モデルの精度を求める"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.9701 ,  0.97   ,  0.97125])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_score\n",
    "cross_val_score(sgd_clf, X_train, y_train_5, cv=3, scoring=\"accuracy\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9701\n",
      "0.97\n",
      "0.97125\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import StratifiedKFold\n",
    "from sklearn.base import clone\n",
    "\n",
    "skfolds = StratifiedKFold(n_splits=3, random_state=42)\n",
    "\n",
    "for train_index, test_index in skfolds.split(X_train, y_train_5):\n",
    "    clone_clf = clone(sgd_clf)\n",
    "    X_train_folds = X_train[train_index]\n",
    "    y_train_folds = (y_train_5[train_index])\n",
    "    X_test_fold = X_train[test_index]\n",
    "    y_test_fold = (y_train_5[test_index])\n",
    "\n",
    "    clone_clf.fit(X_train_folds, y_train_folds)\n",
    "    y_pred = clone_clf.predict(X_test_fold)\n",
    "    n_correct = sum(y_pred == y_test_fold)\n",
    "    print(n_correct / len(y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5でないクラス(1-4,6-9)の精度を求める。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator\n",
    "class Never5Classifier(BaseEstimator):\n",
    "    def fit(self, X, y=None):\n",
    "        pass\n",
    "    def predict(self, X):\n",
    "        return np.zeros((len(X), 1), dtype=bool)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.909  ,  0.90745,  0.9125 ])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "never_5_clf = Never5Classifier()\n",
    "cross_val_score(never_5_clf, X_train, y_train_5, cv=3, scoring=\"accuracy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(deep copy=全部作る, shallow copy=一部作る)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function clone in module sklearn.base:\n",
      "\n",
      "clone(estimator, safe=True)\n",
      "    Constructs a new estimator with the same parameters.\n",
      "    \n",
      "    Clone does a deep copy of the model in an estimator\n",
      "    without actually copying attached data. It yields a new estimator\n",
      "    with the same parameters that has not been fit on any data.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    estimator: estimator object, or list, tuple or set of objects\n",
      "        The estimator or group of estimators to be cloned\n",
      "    \n",
      "    safe: boolean, optional\n",
      "        If safe is false, clone will fall back to a deepcopy on objects\n",
      "        that are not estimators.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(clone)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Confusion Matrix　(p.89)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Confusion Matrix(=混合行列)\n",
    "\n",
    "- Each  row  represents an  actual  class\n",
    "- Each  column  represents a predicted class\n",
    "\n",
    "$$\n",
    "\\begin{array}{|c||c|c|}\n",
    "N=60,000 & Predicted:NO & Predicted:YES \\\\\\hline \n",
    "Actual:NO & 53943[True~Positives(TP)] & 636[False~Negatives(FN)] \\\\\\\n",
    "Actual:YES & 1137[False~Positives(FP)] & 4284[True~Negatives(TN)]\n",
    "\\end{array}\n",
    "$$\n",
    "\n",
    "- 1行1列目(TP)は、数字5でない画像53,943件を正しく5以外と分類できた。\n",
    "- 1行2列目(FN)は、数字5でない画像636件を5と分類した。\n",
    "- 2行1列名(FP)は、数字5画像1137件を、5でないと分類した。\n",
    "- 2行2列名(TN)は、数字5画像4284件を、正しく5と分類できた。\n",
    "\n",
    "\n",
    "\n",
    "- True Negatives - correct prediction\n",
    "- True Positives - correct prediction\n",
    "- False Negatives - incorrect prediction\n",
    "- False Positives - incorrect prediction\n",
    "\n",
    "\n",
    "K-fold cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Figure3-2](./F3-2.png) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'sgd_clf' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-4-7b31475bd1a1>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmodel_selection\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mcross_val_predict\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0my_train_pred\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcross_val_predict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msgd_clf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX_train\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_train_5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mcv\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'sgd_clf' is not defined"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import cross_val_predict\n",
    "\n",
    "y_train_pred = cross_val_predict(sgd_clf, X_train, y_train_5, cv=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'y_train_5' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-5-e763a923c56f>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmetrics\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mconfusion_matrix\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mconfusion_matrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0my_train_5\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_train_pred\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m: name 'y_train_5' is not defined"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "confusion_matrix(y_train_5, y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y_train_perfect_predictions = y_train_5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[54579,     0],\n",
       "       [    0,  5421]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "confusion_matrix(y_train_5, y_train_perfect_predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "confusion matrixの参考サイト\n",
    "https://rasbt.github.io/mlxtend/user_guide/evaluate/confusion_matrix/\n",
    "http://www.baru-san.net/archives/141\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "http://tkdmah.hatenablog.com/entry/2014/02/22/193008"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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