bair_supervised_pca.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Original Paper \n",
    "https://web.stanford.edu/~hastie/Papers/spca_JASA.pdf\n",
    "\n",
    "Steps in brief:\n",
    "1. Compute (univariate) standard regression coefficients for each feature.\n",
    "2. Form a reduced data matrix consisting of only those features whose univariate coefficient exceeds a threshold θ in absolute value (θ is estimated by cross-validation).\n",
    "3. Compute the first (or first few) principal components of the reduced data matrix.\n",
    "4. Use these principal component(s) in a regression model to predict the outcome."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "class spca_model():\n",
    "    \n",
    "    def __init__(model=None, threshold=0, n_components=0):    \n",
    "        self._model = model\n",
    "        self._threshold = threshold\n",
    "        self._n_components = n_components\n",
    "        \n",
    "        self._dropouts = None\n",
    "        self._pca = None\n",
    "        \n",
    "    \n",
    "    def fit_spca_model(self, x, y):\n",
    "        x_extra_dim = x[:, np.newaxis]  # Change dimension from (x,y) to (x,1,y)\n",
    "        # x.reshape(x.shape + (1,))\n",
    "        \n",
    "        self._dropouts = []\n",
    "        \n",
    "        # Fit each feature with the target (predictor) and if the coefficient is less than the threshold, drop it\n",
    "        for i in range(0, x_extra_dim.shape[2]): # iterate over all the features\n",
    "            x_one_feature = x_extra_dim[:, :, i]\n",
    "            self._model.fit(x_one_feature, y)\n",
    "            \n",
    "            if (all([abs(self._model.coef_[0]) < self._threshold])): # Return True if True for all values in the list\n",
    "                self._dropouts.append(i)\n",
    "                \n",
    "        if (len(self._dropouts) == x_extra_dim.shape[2]):  # all features have coef less than the threshold\n",
    "            raise ValueError('Try a smaller threshold')\n",
    "            \n",
    "        if (self._n_components > 0):  # calculate the most important n_components\n",
    "            self._pca = PCA(n_components=self._n_components)\n",
    "        else: # if n_components is not more than 0. then all components are kept\n",
    "            self._pca = PCA(n_components=x_extra_dim.shape[2])\n",
    "        \n",
    "        x_tranform = self._pca.fit_transform(x_extra_dim[:, 0, :])\n",
    "        \n",
    "        self._model = self._model.fit(x_transform, y)\n",
    "        \n",
    "        return self\n",
    "\n",
    "    \n",
    "    def spca_predict(self, x):\n",
    "        # delete from x those features which had coef less than the threshold, and were in the dropout set\n",
    "        trans_x = np.delete(x, self._dropouts, axis=1)  \n",
    "        \n",
    "        # the remaining features have been transformed into components using PCA weights \n",
    "        trans_x = self._pca.transform(trans_x)\n",
    "        \n",
    "        # predict using the spca model\n",
    "        return self._model.predict(trans_x)\n",
    "    \n",
    "    \n",
    "    def get_num_components(self):\n",
    "        # return the number of components after the pca fit\n",
    "        return self._pca.n_components_\n",
    "\n",
    "    \n",
    "    def get_components(self):\n",
    "        # shape : (n_components, n_features)\n",
    "        # Principal axes in feature space, representing the directions of maximum variance in the data.\n",
    "        # Should be run only after the PCA has been run on the training dataset\n",
    "        return self._pca.components_\n",
    "\n",
    "    \n",
    "    def get_coefficients(self):\n",
    "        # return the coefs of the model the data has been fit on\n",
    "        return self._model.coef_\n",
    "    \n",
    "    \n",
    "    def get_score(self, x, y):\n",
    "        # return score of the reduced dimensional data on the model\n",
    "        return self._model.score(x, y)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Using logistic regression for classification\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata('MNIST original')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 784)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_data = mnist.data[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 1, 784)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "784"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_data.shape[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       ...,\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0],\n",
       "       [0, 0, 0, ..., 0, 0, 0]], dtype=uint8)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "new_data[:, 0, :]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=100, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(mnist.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.n_components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       -2.97964359e-04, -2.90656824e-04, -2.63317920e-04, -1.86026386e-04,\n",
       "       -9.86286610e-05, -5.50406293e-05, -2.31401032e-05,  3.29017322e-06,\n",
       "       -5.74756473e-07, -6.03477095e-07, -7.83813224e-07,  6.50947701e-08,\n",
       "        0.00000000e+00,  0.00000000e+00,  0.00000000e+00,  0.00000000e+00])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.28308680e+02, -4.83538412e-28,  6.78896268e-28, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [-4.83538412e-28,  4.28308680e+02, -2.09010917e-28, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 6.78896268e-28, -2.09010917e-28,  4.28308680e+02, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  0.00000000e+00],\n",
       "       ...,\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         4.28308680e+02,  0.00000000e+00,  0.00000000e+00],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         0.00000000e+00,  4.28308680e+02,  0.00000000e+00],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  0.00000000e+00, ...,\n",
       "         0.00000000e+00,  0.00000000e+00,  4.28308680e+02]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "pca.get_covariance()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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