Regularized_Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regularized 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": [
    {
     "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": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/logistic_reg.txt', header=None)\n",
    "data.head()"
   ]
  },
  {
   "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": {},
     "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": 4,
   "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": 4,
     "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": 5,
   "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": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1 + np.exp(1)**(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Regularized cost function\n",
    "def cost(x, theta, y, m, lmbda):\n",
    "    out = sigmoid(x.dot(theta))\n",
    "    reg_term = lmbda*np.sum(theta[1:]**2)/(2*m)\n",
    "    return reg_term - np.sum(np.multiply(y, np.log(out)) + np.multiply(1-y, np.log(1 - out)))/m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(x, y, m, lr, itr, lmbda):\n",
    "    np.random.seed(103)\n",
    "    num_ftrs = len(x[0])\n",
    "    \n",
    "    history = []\n",
    "    \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",
    "        \n",
    "        # No regularization for theta0\n",
    "        theta[0] = theta[0] - lr*diff[0]\n",
    "        \n",
    "        theta[1:] = theta[1:]*(1-lr*(lmbda/m)) - lr*diff[1:]\n",
    "        history.append(cost(x, theta, y, len(x), lmbda))\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\t0.5009146657517323\n",
      "0.01\t100\t0.5186104890175238\n",
      "0.01\t200\t0.5418323361083788\n",
      "0.01\t500\t0.558730401763442\n",
      "0.01\t1000\t0.5475994800091362\n",
      "0.01\t5000\t0.4613469136084279\n",
      "0.01\t10000\t0.4082748733449697\n",
      "0.03\t50\t0.5322960762569476\n",
      "0.03\t100\t0.5535009828845597\n",
      "0.03\t200\t0.557720102751457\n",
      "0.03\t500\t0.5336896823434805\n",
      "0.03\t1000\t0.49768809324282803\n",
      "0.03\t5000\t0.384684180045425\n",
      "0.03\t10000\t0.3744290125775836\n",
      "0.001\t50\t0.4811839602627395\n",
      "0.001\t100\t0.4835370923424499\n",
      "0.001\t200\t0.48812290883685533\n",
      "0.001\t500\t0.5008553102842074\n",
      "0.001\t1000\t0.5185146899694612\n",
      "0.001\t5000\t0.5586889099625457\n",
      "0.001\t10000\t0.5475974976343285\n",
      "0.003\t50\t0.48585487965623175\n",
      "0.003\t100\t0.49254999337987326\n",
      "0.003\t200\t0.504759576827851\n",
      "0.003\t500\t0.5319591444769427\n",
      "0.003\t1000\t0.5532240136651808\n",
      "0.003\t5000\t0.5336930753732095\n",
      "0.003\t10000\t0.497694095509068\n",
      "\n",
      "Lowest error:0.3744290125775836 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",
    "# if we choose large values of lambda then our model will not \n",
    "# perform well on this data as every feature is important\n",
    "lmbda = 0.1\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, lmbda)\n",
    "        # loss on test data\n",
    "        curr_cost = cost(test_x, theta, test_y, len(test_x), lmbda)\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
}