Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "IPython.notebook.set_autosave_interval(60000)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Autosaving every 60 seconds\n"
     ]
    }
   ],
   "source": [
    "%autosave 60\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1 + np.exp(1)**(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(x, theta, y, m):\n",
    "    out = sigmoid(x.dot(theta))\n",
    "    return -np.sum(np.multiply(y, np.log(out)) + np.multiply(1-y, np.log(1 - out)))/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1  2\n",
       "0  34.623660  78.024693  0\n",
       "1  30.286711  43.894998  0\n",
       "2  35.847409  72.902198  0\n",
       "3  60.182599  86.308552  1\n",
       "4  79.032736  75.344376  1"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/logistic_reg.txt', header=None)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.set_style('white')\n",
    "sns.scatterplot(data.iloc[:,0],data.iloc[:,1],hue=data.iloc[:,2]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.49626112, 1.14294811, 0.        ],\n",
       "       [0.43409961, 0.64299778, 0.        ],\n",
       "       [0.51380112, 1.06791102, 0.        ],\n",
       "       [0.86259756, 1.26429458, 1.        ],\n",
       "       [1.13277668, 1.10368538, 1.        ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.array(data.values, dtype = np.float64)\n",
    "\n",
    "# Feature normalization\n",
    "for i in range(len(data[0])):\n",
    "    data[:,i] = data[:,i]/(max(data[:,i]) - min(data[:,i]))\n",
    "\n",
    "data[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x shape\ty_shape\n",
      "(80, 3) (80, 1)\n"
     ]
    }
   ],
   "source": [
    "split = int(0.8*len(data))\n",
    "x = data[:split, :2]\n",
    "x = np.insert(x, 0, 1, axis=1)\n",
    "y = np.expand_dims(data[:split, 2], axis=1)\n",
    "\n",
    "test_x = data[split:, :2]\n",
    "test_x = np.insert(test_x, 0, 1, axis=1)\n",
    "test_y = np.expand_dims(data[split:, 2], axis=1)\n",
    "\n",
    "print('x shape\\ty_shape')\n",
    "print(x.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(x, y, m, lr, itr):\n",
    "    np.random.seed(103)\n",
    "    num_ftrs = len(x[0])\n",
    "    history = []\n",
    "    theta = np.random.rand(num_ftrs) \n",
    "    theta = np.expand_dims(theta, axis=1)\n",
    "    \n",
    "    for i in range(itr):\n",
    "        z = x.dot(theta)\n",
    "        h = sigmoid(z)\n",
    "        diff = x.T.dot(h - y)/m \n",
    "        theta = theta - lr*diff\n",
    "        history.append(cost(x, theta, y, len(y)))\n",
    "    \n",
    "    return theta, history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lr\titr\terror\n",
      "0.01\t50\t0.5007647628075474\n",
      "0.01\t100\t0.5184497880690938\n",
      "0.01\t200\t0.541642067259839\n",
      "0.01\t500\t0.5583944156574662\n",
      "0.01\t1000\t0.5468068342347566\n",
      "0.01\t5000\t0.45227117130382233\n",
      "0.01\t10000\t0.38361767846521844\n",
      "0.03\t50\t0.5321213605262274\n",
      "0.03\t100\t0.5532740250435418\n",
      "0.03\t200\t0.5573117939717102\n",
      "0.03\t500\t0.5322592056336118\n",
      "0.03\t1000\t0.49354998940202544\n",
      "0.03\t5000\t0.3431355386092413\n",
      "0.03\t10000\t0.2860666698180788\n",
      "0.001\t50\t0.4810357472916781\n",
      "0.001\t100\t0.4833893666981138\n",
      "0.001\t200\t0.48797554837802126\n",
      "0.001\t500\t0.5007054173680647\n",
      "0.001\t1000\t0.5183540102268538\n",
      "0.001\t5000\t0.5583527727040059\n",
      "0.001\t10000\t0.5468047983662037\n",
      "0.003\t50\t0.4857074320771\n",
      "0.003\t100\t0.49240231040041077\n",
      "0.003\t200\t0.504607990534379\n",
      "0.003\t500\t0.5317844402891889\n",
      "0.003\t1000\t0.5529967139018966\n",
      "0.003\t5000\t0.5322625236223884\n",
      "0.003\t10000\t0.49355614262969355\n",
      "\n",
      "Lowest error:0.2860666698180788 for lr:0.03 and itr:10000\n",
      "\n",
      "Plotting graph for lowest error...\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "best_theta = best_history = None\n",
    "best_lr = best_itr = 0\n",
    "prev_cost = 1\n",
    "\n",
    "print('lr\\titr\\terror')\n",
    "for lr in [0.01, 0.03, 0.001, 0.003]:\n",
    "    for itr in [50, 100, 200, 500, 1000, 5000, 10000]:\n",
    "        theta, history = train(x, y, len(x), lr, itr)\n",
    "        # loss on test data\n",
    "        curr_cost = cost(test_x, theta, test_y, len(test_x))\n",
    "        print('{}\\t{}\\t{}'.format(lr, itr, curr_cost))\n",
    "        if curr_cost < prev_cost:\n",
    "            prev_cost = curr_cost\n",
    "            best_lr = lr\n",
    "            best_itr = itr\n",
    "            best_theta = theta\n",
    "            best_history = history\n",
    "            \n",
    "print('\\nLowest error:{} for lr:{} and itr:{}'.format(prev_cost, best_lr, best_itr))\n",
    "\n",
    "print('\\nPlotting graph for lowest error...')\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "fig.set_figheight(5)\n",
    "fig.set_figwidth(10)\n",
    "\n",
    "ax.plot(range(best_itr), best_history, 'g')\n",
    "ax.set_xlabel('Iteration')\n",
    "ax.set_ylabel('Cost')\n",
    "ax.title.set_text('Cost v/s Iteration')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "output\tactual\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(0.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(0.0, 0.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(0.0, 0.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(0.0, 0.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(1.0, 1.0)\n",
      "(0.0, 1.0)\n",
      "(1.0, 1.0)\n"
     ]
    }
   ],
   "source": [
    "# Checking results manually\n",
    "best_out = sigmoid(test_x.dot(best_theta))\n",
    "print('output\\tactual')\n",
    "print(*[(np.round(best_out[i])[0], test_y[i][0]) for i in range(len(test_x))], sep='\\n')"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}