ml-ex2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This exercise is described in [ex2.pdf](data/ml-ex2/ex2.pdf)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from matplotlib import colors\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from scipy.special import logit\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Unregularized logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Admission data: \n",
    "# - exam 1 score (x1) \n",
    "# - exam 2 score (x2)\n",
    "# - admitted (y)\n",
    "data = np.loadtxt('data/ml-ex2/ex2data1.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separate features (x1, x2) from target (y)\n",
    "X, y = np.hsplit(data, np.array([2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LogisticRegression estimator expect an y row vector\n",
    "y = y.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1000000000.0, class_weight=None, dual=False,\n",
       "          fit_intercept=True, intercept_scaling=1, max_iter=100,\n",
       "          multi_class='warn', n_jobs=None, penalty='l2', random_state=None,\n",
       "          solver='lbfgs', tol=0.0001, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use 'lbfgs' solver for logistic regression as this is what Octave fminunc does.\n",
    "# Parameter C ist the inverse regularization strength (high values = low regularization).\n",
    "clf = LogisticRegression(C=1e9, solver='lbfgs')\n",
    "clf.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta0 = clf.intercept_[0]\n",
    "theta1 = clf.coef_[0,0]\n",
    "theta2 = clf.coef_[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Computes x2 at y = logit(0.5) from x1 and model parameters\n",
    "# based on equation y = sigmoid(theta0 + theta1*x1 + theta2*x2)\n",
    "# where logit is the inverse of sigmoid.\n",
    "# (used for computing the linear decision boundary)\n",
    "def x2(x1):\n",
    "    return (logit(0.5) - theta0 - theta1*x1) / theta2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1_min = X[:,0].min()\n",
    "x1_max = X[:,0].max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# x1 and x2 data of linear decision boundary\n",
    "x1_plot = np.array([x1_min, x1_max])\n",
    "x2_plot = x2(x1_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f78c2ed2ef0>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Mask for selecting positive and negative examples\n",
    "y_pos = y == 1\n",
    "y_neg = y == 0\n",
    "\n",
    "# Plot examples and decision boundary\n",
    "ax.plot(X[y_pos,0], X[y_pos,1], 'b+', label='Admitted')\n",
    "ax.plot(X[y_neg,0], X[y_neg,1], 'yo', label='Not admitted')\n",
    "ax.set_xlabel('Exam 1 score')\n",
    "ax.set_ylabel('Exam 2 score')\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "# Plot decision boundary\n",
    "ax.plot(x1_plot, x2_plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = np.array([\n",
    "    [45., 85.],\n",
    "    [50., 50.],\n",
    "    [80., 80.]\n",
    "])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 0., 1.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict class\n",
    "clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.23709868e-01, 7.76290132e-01],\n",
       "       [9.91642300e-01, 8.35769979e-03],\n",
       "       [5.78239123e-04, 9.99421761e-01]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict class probabilities\n",
    "clf.predict_proba(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta0 = clf.intercept_[0]\n",
    "theta1 = clf.coef_[0,0]\n",
    "theta2 = clf.coef_[0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-25.16138567101981, 0.20623222395628113, 0.20147190519771901)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta0, theta1, theta2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.89"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Classification accuracy on training set\n",
    "clf.score(X, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularized logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Microchip test: \n",
    "# - test 1 (x1) \n",
    "# - test 2 (x2)\n",
    "# - accepted=1, rejected=0 (y)\n",
    "data = np.loadtxt('data/ml-ex2/ex2data2.txt', delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LogisticRegression estimator expect an y row vector\n",
    "X, y = np.hsplit(data, np.array([2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Logistic regression estimator requires an y row vector\n",
    "y = y.ravel()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f78c2e18940>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "# Mask for selecting positive and negative examples\n",
    "y_pos = y == 1\n",
    "y_neg = y == 0\n",
    "\n",
    "# Plot examples\n",
    "ax.plot(X[y_pos,0], X[y_pos,1], 'b+', label='Accepted')\n",
    "ax.plot(X[y_neg,0], X[y_neg,1], 'yo', label='Rejected')\n",
    "ax.set_xlabel('Microchip test 1')\n",
    "ax.set_ylabel('Microchip test 2')\n",
    "ax.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pipeline(memory=None,\n",
       "     steps=[('poly', PolynomialFeatures(degree=6, include_bias=False, interaction_only=False)), ('scaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('clf', LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='warn',\n",
       "          n_jobs=None, penalty='l2', random_state=None, solver='lbfgs',\n",
       "          tol=0.0001, verbose=0, warm_start=False))])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Preprocessor to include polynomial features up to degree 6\n",
    "poly = PolynomialFeatures(6, include_bias=False)\n",
    "\n",
    "# Mean and standard deviation scaler\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# Logistic regression classifier. \n",
    "# - C=1.0 will result in good fit\n",
    "# - C=1e4 will result in overfit (to little regularization)\n",
    "# - C=1e-2 will result in underfit (to much regularization)\n",
    "clf = LogisticRegression(C=1.0, solver='lbfgs')\n",
    "\n",
    "# Pipeline of polynomial feature generator, feature scaler and linear regressor\n",
    "model = Pipeline([('poly', poly), ('scaler', scaler), ('clf', clf)])\n",
    "\n",
    "# Fit data to model\n",
    "model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8305084745762712"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Classification accuracy on training set\n",
    "model.score(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid = np.mgrid[-1:1:500j, -1:1:500j]\n",
    "\n",
    "# Compute acceptance probabilities on 500*500 grid \n",
    "X_grid = np.c_[grid[0].ravel(), grid[1].ravel()]\n",
    "y_grid = model.predict(X_grid).reshape(grid[0].shape)\n",
    "\n",
    "# Plot decision boundary on previous figure\n",
    "cs = ax.contour(grid[0], grid[1], y_grid, 'g-', levels=[0.5])\n",
    "ax.clabel(cs)\n",
    "\n",
    "# Show previous figure with decision boundary\n",
    "fig"
   ]
  }
 ],
 "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}