log-reg.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as scs\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generate data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs = np.array(range(10, 200, 20))\n",
    "ys = np.array([0,0,0,0,1,0,1,0,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.scatter(xs, ys)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(xs, b1):\n",
    "    return 1 / (1 + np.exp( -1 * xs * b1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss(ys, phs):\n",
    "    # negative log loss\n",
    "    losses = (ys * np.log(phs)) + ((1 - ys) * np.log(1 - phs))\n",
    "    return -1 * losses # [~np.isnan(losses) & ~np.isinf(losses)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/chyld/.conda/envs/py37/lib/python3.7/site-packages/sklearn/linear_model/logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
      "  FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "model = LogisticRegression().fit(xs.reshape(10,1), ys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.01007969]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.00497899])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.28819183, 0.33123861, 0.37730698, 0.42570398, 0.47556773,\n",
       "       0.52592344, 0.57575732, 0.62409693, 0.6700847 , 0.7130333 ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(xs.reshape(10,1))[:,1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loss as function of $ \\beta $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/chyld/.conda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: divide by zero encountered in log\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/Users/chyld/.conda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in multiply\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    }
   ],
   "source": [
    "betas = list(range(-2,4))\n",
    "predictions = np.array([predict(xs, b) for b in betas])\n",
    "losses = np.array([loss(ys, predict(xs, b)) for b in betas])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[-2, -1, 0, 1, 2, 3]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "betas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/chyld/.conda/envs/py37/lib/python3.7/site-packages/matplotlib/cbook/__init__.py:1166: RuntimeWarning: invalid value encountered in double_scalars\n",
      "  notch_min = med - 1.57 * iqr / np.sqrt(N)\n",
      "/Users/chyld/.conda/envs/py37/lib/python3.7/site-packages/numpy/lib/function_base.py:3826: RuntimeWarning: Invalid value encountered in percentile\n",
      "  interpolation=interpolation)\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(14, 7))\n",
    "ax = fig.add_subplot(111)\n",
    "bp = ax.boxplot(losses, patch_artist=True)\n",
    "for box in bp['boxes']:\n",
    "    box.set(color='#ff33cc', linewidth=1)\n",
    "    box.set(facecolor='#dddddd', alpha=0.5)\n",
    "for whisker in bp['whiskers']:\n",
    "    whisker.set(color='blue', linewidth=1, linestyle='--')\n",
    "for cap in bp['caps']:\n",
    "    cap.set(color='blue', linewidth=1)\n",
    "for median in bp['medians']:\n",
    "    median.set(color='green', linewidth=1, linestyle='--')\n",
    "for flier in bp['fliers']:\n",
    "    flier.set(color='black', marker='*', alpha=0.7)\n",
    "ax.set_xticklabels(betas)\n",
    "ax.set_xlabel('Beta')\n",
    "ax.set_ylabel('Loss')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2.06115362e-009, 8.75651076e-027, 3.72007598e-044,\n",
       "        1.58042006e-061, 6.71418429e-079, 2.85242334e-096,\n",
       "        1.21181048e-113, 5.14820022e-131, 2.18713783e-148,\n",
       "        9.29173632e-166],\n",
       "       [4.53978687e-005, 9.35762297e-014, 1.92874985e-022,\n",
       "        3.97544974e-031, 8.19401262e-040, 1.68891188e-048,\n",
       "        3.48110684e-057, 7.17509597e-066, 1.47889751e-074,\n",
       "        3.04823495e-083],\n",
       "       [5.00000000e-001, 5.00000000e-001, 5.00000000e-001,\n",
       "        5.00000000e-001, 5.00000000e-001, 5.00000000e-001,\n",
       "        5.00000000e-001, 5.00000000e-001, 5.00000000e-001,\n",
       "        5.00000000e-001],\n",
       "       [9.99954602e-001, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000],\n",
       "       [9.99999998e-001, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000],\n",
       "       [1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000, 1.00000000e+000, 1.00000000e+000,\n",
       "        1.00000000e+000]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "predictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.06115358e-09, -0.00000000e+00, -0.00000000e+00,\n",
       "        -0.00000000e+00,  1.80000000e+02, -0.00000000e+00,\n",
       "         2.60000000e+02, -0.00000000e+00,  3.40000000e+02,\n",
       "         3.80000000e+02],\n",
       "       [ 4.53988992e-05,  9.35918010e-14, -0.00000000e+00,\n",
       "        -0.00000000e+00,  9.00000000e+01, -0.00000000e+00,\n",
       "         1.30000000e+02, -0.00000000e+00,  1.70000000e+02,\n",
       "         1.90000000e+02],\n",
       "       [ 6.93147181e-01,  6.93147181e-01,  6.93147181e-01,\n",
       "         6.93147181e-01,  6.93147181e-01,  6.93147181e-01,\n",
       "         6.93147181e-01,  6.93147181e-01,  6.93147181e-01,\n",
       "         6.93147181e-01],\n",
       "       [ 1.00000454e+01,  3.00010206e+01,             inf,\n",
       "                    inf,             nan,             inf,\n",
       "                    nan,             inf,             nan,\n",
       "                    nan],\n",
       "       [ 2.00000000e+01,             inf,             inf,\n",
       "                    inf,             nan,             inf,\n",
       "                    nan,             inf,             nan,\n",
       "                    nan],\n",
       "       [ 3.00010206e+01,             inf,             inf,\n",
       "                    inf,             nan,             inf,\n",
       "                    nan,             inf,             nan,\n",
       "                    nan]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "losses"
   ]
  },
  {
   "cell_type": "code",
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