sgd.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating Fake Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.utils import shuffle\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, Y = make_blobs(n_samples=300, centers=2, n_features=2, cluster_std=5, random_state=11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Data"
   ]
  },
  {
   "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": [
    "from matplotlib import pyplot as plt\n",
    "from pandas import DataFrame \n",
    "df = DataFrame(dict(x=X[:,0], y=X[:,1], label=Y))\n",
    "colors = {0:'blue', 1:'orange'}\n",
    "fig, ax = plt.subplots()\n",
    "grouped = df.groupby('label')\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])\n",
    "plt.xlabel('X_1')\n",
    "plt.ylabel('X_2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Splitting into batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def next_batch(X, Y, batch_size):\n",
    "    for i in np.arange(0, X.shape[0], batch_size):\n",
    "        yield (X[i:i + batch_size], Y[i:i + batch_size])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding column of 1's "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(300, 3)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.c_[np.ones((X.shape[0])), X]\n",
    "X.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hx(W,X):\n",
    "    return sigmoid(np.dot(X,W))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cost Function - Binary Cross Entropy "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost(W, X, Y):\n",
    "    y_pred = hx(W,X)\n",
    "    return -1 * sum(Y*np.log(y_pred) + (1-Y)*np.log(1-y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stochastic Gradient Descent"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def grad(W, X, Y):\n",
    "    y_pred = hx(W,X)\n",
    "    A = (Y*(1-y_pred) - (1-Y)*y_pred)\n",
    "    g = -1* np.dot(A.T,X)\n",
    "    return g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(W_new, W_prev, lr, batch_size, epochs):\n",
    "    X_, Y_ = shuffle(X, Y, random_state=0)\n",
    "    for e in range(epochs):\n",
    "        epoch_loss = []\n",
    "        X_, Y_ = shuffle(X_, Y_, random_state=0)\n",
    "        for (batchX, batchY) in next_batch(X_, Y_, batch_size):\n",
    "            W_prev = W_new\n",
    "            epoch_loss.append(cost(W_prev, batchX, batchY))\n",
    "            gradients = grad(W_prev, batchX, batchY)\n",
    "            W_new = W_prev - lr*gradients\n",
    "        print(np.average(epoch_loss))\n",
    "    return W_new"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initializing Weights & Bias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W = np.random.uniform(size=(X.shape[1],))\n",
    "W.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training the Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.79618896 0.4163837  0.42391672]\n",
      "6.277384446178855\n",
      "5.743854541290189\n",
      "5.639645113634937\n",
      "5.470853335391083\n",
      "5.667962099033007\n",
      "5.28981499238036\n",
      "5.271342725834096\n",
      "5.060368761481374\n",
      "5.446976524735743\n",
      "5.066447704414417\n",
      "5.09547652563199\n",
      "5.027047324020139\n",
      "5.231413878163542\n",
      "4.988553649645022\n",
      "5.045966239495252\n",
      "5.114093205881277\n",
      "5.24313649711587\n",
      "5.3309800879511595\n",
      "5.2369933729138705\n",
      "4.931357222546931\n",
      "5.141072913940974\n",
      "4.865177946360237\n",
      "5.159259956251705\n",
      "4.9850013574989935\n",
      "5.075992543432262\n",
      "5.257537980731875\n",
      "5.15220734911969\n",
      "5.376113028226739\n",
      "5.01790696023796\n",
      "4.91743150129637\n",
      "5.155592756181093\n",
      "4.778496875740468\n",
      "5.170830308497642\n",
      "4.982057737386109\n",
      "5.065383224896023\n",
      "5.130301783329287\n",
      "5.0560422794900335\n",
      "4.751542045996459\n",
      "5.044836198314092\n",
      "5.200065208594642\n",
      "5.285956700133218\n",
      "4.69607623817095\n",
      "5.1110131343684895\n",
      "4.929261653440459\n",
      "5.508577234972032\n",
      "4.9295442093408335\n",
      "5.35853341436791\n",
      "5.109882297828997\n",
      "5.268900506923824\n",
      "5.0553568625861995\n",
      "5.127108057053507\n",
      "5.256180863878795\n",
      "5.2017470229439295\n",
      "5.29706022610866\n",
      "4.842578732589242\n",
      "5.216497984078021\n",
      "5.167172158840554\n",
      "5.030913544155235\n",
      "4.9208154561894215\n",
      "5.0286895579435775\n",
      "5.254927983516582\n",
      "5.01657084246088\n",
      "4.902782163580072\n",
      "4.952060238428389\n",
      "4.9191214387250035\n",
      "5.027098170280329\n",
      "5.077946337475286\n",
      "4.880098287861289\n",
      "4.944972140093644\n",
      "5.052666303168795\n",
      "5.081615975832211\n",
      "5.182569862898558\n",
      "4.9697239615921625\n",
      "5.056706134894904\n",
      "5.110368058329958\n",
      "4.996883358551884\n",
      "4.989696640078847\n",
      "4.858898302441649\n",
      "4.930715531754518\n",
      "5.009314794537656\n",
      "5.127984153485331\n",
      "5.0231049124602825\n",
      "5.254008279820028\n",
      "5.014073801135062\n",
      "4.97986671455312\n",
      "5.05243719762335\n",
      "5.0420997708089415\n",
      "5.069451589063102\n",
      "5.150257226697879\n",
      "5.164400634677876\n",
      "5.039134823534483\n",
      "4.9883474157043795\n",
      "5.132433782589542\n",
      "4.891167385232467\n",
      "5.062085674381252\n",
      "5.2087055067642165\n",
      "4.955120478076216\n",
      "4.88214965225135\n",
      "4.935119155279668\n",
      "5.4527388101645755\n",
      "4.902647474574163\n",
      "4.973218626980669\n",
      "4.969125747240431\n",
      "5.034819845305565\n",
      "5.11158072777152\n",
      "5.052709686640736\n",
      "4.968840505649011\n",
      "5.088612053925859\n",
      "4.915818444090352\n",
      "5.093157727293972\n",
      "5.033660011718062\n",
      "5.223412724166921\n",
      "5.1077816665230475\n",
      "5.135494856877415\n",
      "4.989777059244171\n",
      "5.165527490515357\n",
      "5.327764783138228\n",
      "5.019080784749545\n",
      "5.0239554594473805\n",
      "5.026682139880581\n",
      "5.159710856114193\n",
      "5.027795318281852\n",
      "4.988648104694423\n",
      "5.012928309587274\n",
      "5.081666714554431\n",
      "5.272117622609143\n",
      "4.851869972177484\n",
      "4.956969286562633\n",
      "5.025160410234134\n",
      "4.993677569943672\n",
      "5.099870584911604\n",
      "5.096181311604027\n",
      "5.236923964162504\n",
      "4.903674873885619\n",
      "5.075807820064275\n",
      "4.701673307737802\n",
      "5.299083765240716\n",
      "5.112201692629844\n",
      "5.057198863500682\n",
      "5.213612968874003\n",
      "5.1198465312517225\n",
      "4.928097399784619\n",
      "4.991964359552881\n",
      "4.994824548764347\n",
      "5.049272339126923\n",
      "4.942713247937617\n",
      "4.91913758023255\n",
      "5.43143326229052\n",
      "5.116114463071936\n",
      "4.9625898877661445\n",
      "5.042137105313292\n",
      "5.157805681662321\n",
      "5.04896325685934\n",
      "5.018982423826876\n",
      "5.185034061711793\n",
      "5.032465453425752\n",
      "4.897108003638827\n",
      "4.95421678149162\n",
      "5.259006286037971\n",
      "5.182717981721985\n",
      "4.884826442197778\n",
      "5.156842877561891\n",
      "5.047645060816286\n",
      "5.050121866311711\n",
      "4.869794749038038\n",
      "4.9957190876138835\n",
      "5.022988953794398\n",
      "5.002839753440677\n",
      "4.881319490767778\n",
      "5.055591006717888\n",
      "5.015670050297785\n",
      "5.013392499945725\n",
      "4.989724363452584\n",
      "4.880412359751283\n",
      "5.416224099805669\n",
      "5.2867392415724135\n",
      "5.11414942585176\n",
      "5.079966239068073\n",
      "4.925427043815789\n",
      "5.145176957835869\n",
      "5.130160451160554\n",
      "5.024814422423505\n",
      "4.958769936817604\n",
      "4.81843182784822\n",
      "5.34842232805925\n",
      "5.279335054775109\n",
      "5.107921381756868\n",
      "5.15079791674754\n",
      "5.096406330816437\n",
      "5.00585692466524\n",
      "5.200218860079871\n",
      "4.96229644142354\n",
      "4.937523034036624\n",
      "5.174090668819386\n",
      "5.1400977102309175\n",
      "5.1319926651455186\n",
      "5.048127875476851\n",
      "5.416048064604175\n",
      "5.057120736099771\n",
      "4.864273959307718\n",
      "[2.38150361 0.22263106 0.53666744]\n"
     ]
    }
   ],
   "source": [
    "print(W)\n",
    "W = sgd(W, W, .009, 32, 200)\n",
    "print(W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing the Result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def graph(formula, x_range):  \n",
    "    x = np.array(x_range)  \n",
    "    y = formula(x)  \n",
    "    plt.plot(x, y)  \n",
    "    \n",
    "def my_formula(x):\n",
    "    return (-W[0]-W[1]*x)/W[2]\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from pandas import DataFrame \n",
    "df = DataFrame(dict(x=X[:,1], y=X[:,2], label=Y))\n",
    "colors = {0:'blue', 1:'orange'}\n",
    "fig, ax = plt.subplots()\n",
    "grouped = df.groupby('label')\n",
    "for key, group in grouped:\n",
    "    group.plot(ax=ax, kind='scatter', x='x', y='y', label=key, color=colors[key])\n",
    "graph(my_formula, range(-20,15))\n",
    "plt.xlabel('X_1')\n",
    "plt.ylabel('X_2')\n",
    "plt.show()"
   ]
  }
 ],
 "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
}