{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The purpose of this notebook is to validate ``macaw``'s logistic regression code. The original example is available in scikit-learn's documentation here: http://scikit-learn.org/stable/auto_examples/linear_model/plot_logistic.html#sphx-glr-auto-examples-linear-model-plot-logistic-py "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from macaw.objective_functions import LogisticRegression\n",
    "from macaw.models import LogisticModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generate some toy data\n",
    "xmin, xmax = -5, 5\n",
    "n_samples = 100\n",
    "np.random.seed(0)\n",
    "X = np.random.normal(size=n_samples)\n",
    "y = (X > 0).astype(np.float)\n",
    "X[X > 0] *= 4\n",
    "X += .3 * np.random.normal(size=n_samples)\n",
    "X = X[:, np.newaxis]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "loss = LogisticRegression(y=y, X=X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = loss.fit(x0=np.random.rand(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.90880141, -1.64912633])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "res.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x113b5bcc0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ACCI7g2FqxAIiiOwMhqkRC4ggsi6GqRELiCCyLoapEQuIILIuhqkR3ybv9da7X0RyIvIf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\nLAsIY0xZFhDGmLIsIIwxZf1/TI/Yq08S5+AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113b5b518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(1, figsize=(4, 3))\n",
    "plt.scatter(X.ravel(), y, color='black', alpha=.4)\n",
    "X_test = np.linspace(-5, 10, 300)\n",
    "model = LogisticModel(X_test)\n",
    "plt.plot(X_test, model(res.x[0], res.x[1]), color='red', linewidth=2, alpha=.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
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