From 25543404dfb936a2135d7e567559ba55fbb1e22d Mon Sep 17 00:00:00 2001
From: epicalyx <32308101+epicalyx@users.noreply.github.com>
Date: Wed, 3 Oct 2018 19:12:22 +0530
Subject: [PATCH 1/2] gradient_descent/python/gradient_descent.ipynb

Implementation of Gradient Descent in python 3
---
 .../Gradient Descent Description.docx         |  Bin 0 -> 80893 bytes
 .../gradient_descent.ipynb                    | 1151 +++++++++++++++++
 2 files changed, 1151 insertions(+)
 create mode 100644 linear_regression_class/Gradient Descent Description.docx
 create mode 100644 linear_regression_class/gradient_descent.ipynb

diff --git a/linear_regression_class/Gradient Descent Description.docx b/linear_regression_class/Gradient Descent Description.docx
new file mode 100644
index 0000000000000000000000000000000000000000..82ab773d377762999f1200ca1dd06f349eab986d
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diff --git a/linear_regression_class/gradient_descent.ipynb b/linear_regression_class/gradient_descent.ipynb
new file mode 100644
index 00000000..378164af
--- /dev/null
+++ b/linear_regression_class/gradient_descent.ipynb
@@ -0,0 +1,1151 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Implementation of Gradient Descent Algorithm from scratch"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Importing all the required libraries\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "import pylab\n",
+    "import seaborn as sns\n",
+    "import numpy as np\n",
+    "import random\n",
+    "from scipy import stats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "J= [32.07273388]\n",
+      "J= [6.73719046]\n",
+      "J= [5.93159357]\n",
+      "J= [5.90115471]\n",
+      "J= [5.89522859]\n",
+      "J= [5.89009494]\n",
+      "J= [5.88500416]\n",
+      "J= [5.87993248]\n",
+      "J= [5.87487909]\n",
+      "J= [5.86984391]\n",
+      "J= [5.86482687]\n",
+      "J= [5.85982789]\n",
+      "J= [5.85484692]\n",
+      "J= [5.84988389]\n",
+      "J= [5.84493874]\n",
+      "J= [5.8400114]\n",
+      "J= [5.83510181]\n",
+      "J= [5.8302099]\n",
+      "J= [5.82533562]\n",
+      "J= [5.82047889]\n",
+      "J= [5.81563965]\n",
+      "J= [5.81081784]\n",
+      "J= [5.8060134]\n",
+      "J= [5.80122627]\n",
+      "J= [5.79645638]\n",
+      "J= [5.79170367]\n",
+      "J= [5.78696808]\n",
+      "J= [5.78224955]\n",
+      "J= [5.77754801]\n",
+      "J= [5.77286341]\n",
+      "J= [5.76819568]\n",
+      "J= [5.76354477]\n",
+      "J= [5.75891061]\n",
+      "J= [5.75429313]\n",
+      "J= [5.7496923]\n",
+      "J= [5.74510803]\n",
+      "J= [5.74054027]\n",
+      "J= [5.73598897]\n",
+      "J= [5.73145406]\n",
+      "J= [5.72693549]\n",
+      "J= [5.72243319]\n",
+      "J= [5.71794711]\n",
+      "J= [5.71347718]\n",
+      "J= [5.70902336]\n",
+      "J= [5.70458558]\n",
+      "J= [5.70016379]\n",
+      "J= [5.69575792]\n",
+      "J= [5.69136792]\n",
+      "J= [5.68699373]\n",
+      "J= [5.6826353]\n",
+      "J= [5.67829257]\n",
+      "J= [5.67396548]\n",
+      "J= [5.66965398]\n",
+      "J= [5.665358]\n",
+      "J= [5.6610775]\n",
+      "J= [5.65681242]\n",
+      "J= [5.6525627]\n",
+      "J= [5.64832829]\n",
+      "J= [5.64410913]\n",
+      "J= [5.63990517]\n",
+      "J= [5.63571635]\n",
+      "J= [5.63154261]\n",
+      "J= [5.62738391]\n",
+      "J= [5.6232402]\n",
+      "J= [5.6191114]\n",
+      "J= [5.61499748]\n",
+      "J= [5.61089837]\n",
+      "J= [5.60681403]\n",
+      "J= [5.60274441]\n",
+      "J= [5.59868944]\n",
+      "J= [5.59464907]\n",
+      "J= [5.59062326]\n",
+      "J= [5.58661195]\n",
+      "J= [5.58261509]\n",
+      "J= [5.57863263]\n",
+      "J= [5.57466451]\n",
+      "J= [5.57071068]\n",
+      "J= [5.56677109]\n",
+      "J= [5.5628457]\n",
+      "J= [5.55893444]\n",
+      "J= [5.55503727]\n",
+      "J= [5.55115414]\n",
+      "J= [5.547285]\n",
+      "J= [5.54342979]\n",
+      "J= [5.53958847]\n",
+      "J= [5.53576098]\n",
+      "J= [5.53194728]\n",
+      "J= [5.52814732]\n",
+      "J= [5.52436105]\n",
+      "J= [5.52058841]\n",
+      "J= [5.51682936]\n",
+      "J= [5.51308385]\n",
+      "J= [5.50935183]\n",
+      "J= [5.50563326]\n",
+      "J= [5.50192808]\n",
+      "J= [5.49823624]\n",
+      "J= [5.49455771]\n",
+      "J= [5.49089242]\n",
+      "J= [5.48724033]\n",
+      "J= [5.4836014]\n",
+      "J= [5.47997558]\n",
+      "J= [5.47636282]\n",
+      "J= [5.47276307]\n",
+      "J= [5.46917628]\n",
+      "J= [5.46560242]\n",
+      "J= [5.46204143]\n",
+      "J= [5.45849326]\n",
+      "J= [5.45495788]\n",
+      "J= [5.45143522]\n",
+      "J= [5.44792526]\n",
+      "J= [5.44442794]\n",
+      "J= [5.44094322]\n",
+      "J= [5.43747105]\n",
+      "J= [5.43401138]\n",
+      "J= [5.43056418]\n",
+      "J= [5.42712939]\n",
+      "J= [5.42370698]\n",
+      "J= [5.42029689]\n",
+      "J= [5.41689909]\n",
+      "J= [5.41351352]\n",
+      "J= [5.41014015]\n",
+      "J= [5.40677893]\n",
+      "J= [5.40342982]\n",
+      "J= [5.40009277]\n",
+      "J= [5.39676774]\n",
+      "J= [5.39345469]\n",
+      "J= [5.39015357]\n",
+      "J= [5.38686434]\n",
+      "J= [5.38358696]\n",
+      "J= [5.38032138]\n",
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+      "J= [5.37382547]\n",
+      "J= [5.37059505]\n",
+      "J= [5.36737627]\n",
+      "J= [5.36416908]\n",
+      "J= [5.36097345]\n",
+      "J= [5.35778933]\n",
+      "J= [5.35461667]\n",
+      "J= [5.35145544]\n",
+      "J= [5.3483056]\n",
+      "J= [5.34516711]\n",
+      "J= [5.34203991]\n",
+      "J= [5.33892399]\n",
+      "J= [5.33581928]\n",
+      "J= [5.33272576]\n",
+      "J= [5.32964339]\n",
+      "J= [5.32657211]\n",
+      "J= [5.3235119]\n",
+      "J= [5.32046271]\n",
+      "J= [5.3174245]\n",
+      "J= [5.31439724]\n",
+      "J= [5.31138088]\n",
+      "J= [5.30837538]\n",
+      "J= [5.30538071]\n",
+      "J= [5.30239683]\n",
+      "J= [5.2994237]\n",
+      "J= [5.29646127]\n",
+      "J= [5.29350951]\n",
+      "J= [5.29056839]\n",
+      "J= [5.28763786]\n",
+      "J= [5.28471789]\n",
+      "J= [5.28180843]\n",
+      "J= [5.27890945]\n",
+      "J= [5.27602092]\n",
+      "J= [5.27314279]\n",
+      "J= [5.27027503]\n",
+      "J= [5.26741759]\n",
+      "J= [5.26457045]\n",
+      "J= [5.26173356]\n",
+      "J= [5.2589069]\n",
+      "J= [5.25609041]\n",
+      "J= [5.25328407]\n",
+      "J= [5.25048783]\n",
+      "J= [5.24770167]\n",
+      "J= [5.24492555]\n",
+      "J= [5.24215942]\n",
+      "J= [5.23940326]\n",
+      "J= [5.23665702]\n",
+      "J= [5.23392068]\n",
+      "J= [5.23119419]\n",
+      "J= [5.22847752]\n",
+      "J= [5.22577064]\n",
+      "J= [5.22307351]\n",
+      "J= [5.22038609]\n",
+      "J= [5.21770835]\n",
+      "J= [5.21504026]\n",
+      "J= [5.21238178]\n",
+      "J= [5.20973288]\n",
+      "J= [5.20709351]\n",
+      "J= [5.20446365]\n",
+      "J= [5.20184327]\n",
+      "J= [5.19923232]\n",
+      "J= [5.19663078]\n",
+      "J= [5.19403861]\n",
+      "J= [5.19145577]\n",
+      "J= [5.18888224]\n",
+      "J= [5.18631798]\n",
+      "J= [5.18376295]\n",
+      "J= [5.18121713]\n",
+      "J= [5.17868048]\n",
+      "J= [5.17615296]\n",
+      "J= [5.17363455]\n",
+      "J= [5.17112521]\n",
+      "J= [5.16862491]\n",
+      "J= [5.16613361]\n",
+      "J= [5.16365129]\n",
+      "J= [5.16117791]\n",
+      "J= [5.15871344]\n",
+      "J= [5.15625784]\n",
+      "J= [5.15381109]\n",
+      "J= [5.15137315]\n",
+      "J= [5.148944]\n",
+      "J= [5.14652359]\n",
+      "J= [5.1441119]\n",
+      "J= [5.1417089]\n",
+      "J= [5.13931455]\n",
+      "J= [5.13692883]\n",
+      "J= [5.1345517]\n",
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+      "J= [5.1298231]\n",
+      "J= [5.12747157]\n",
+      "J= [5.1251285]\n",
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+      "J= [4.52537919]\n",
+      "J= [4.52520483]\n",
+      "J= [4.52503109]\n",
+      "J= [4.52485799]\n",
+      "J= [4.5246855]\n",
+      "J= [4.52451364]\n",
+      "J= [4.52434239]\n",
+      "J= [4.52417177]\n",
+      "J= [4.52400175]\n",
+      "J= [4.52383235]\n",
+      "J= [4.52366356]\n",
+      "J= [4.52349538]\n",
+      "J= [4.5233278]\n",
+      "J= [4.52316083]\n",
+      "J= [4.52299446]\n",
+      "J= [4.52282868]\n",
+      "J= [4.52266351]\n",
+      "J= [4.52249893]\n",
+      "J= [4.52233494]\n",
+      "J= [4.52217154]\n",
+      "J= [4.52200874]\n",
+      "J= [4.52184651]\n",
+      "J= [4.52168488]\n",
+      "J= [4.52152382]\n",
+      "J= [4.52136335]\n",
+      "J= [4.52120345]\n",
+      "J= [4.52104413]\n",
+      "J= [4.52088538]\n",
+      "J= [4.5207272]\n",
+      "J= [4.5205696]\n",
+      "J= [4.52041256]\n",
+      "J= [4.52025609]\n",
+      "J= [4.52010018]\n",
+      "J= [4.51994483]\n",
+      "J= [4.51979004]\n",
+      "J= [4.51963581]\n",
+      "J= [4.51948214]\n",
+      "J= [4.51932902]\n",
+      "J= [4.51917645]\n",
+      "J= [4.51902443]\n",
+      "J= [4.51887295]\n",
+      "J= [4.51872203]\n",
+      "J= [4.51857164]\n",
+      "J= [4.5184218]\n",
+      "J= [4.5182725]\n",
+      "J= [4.51812373]\n",
+      "J= [4.51797551]\n",
+      "J= [4.51782781]\n",
+      "J= [4.51768065]\n",
+      "J= [4.51753402]\n",
+      "J= [4.51738791]\n",
+      "J= [4.51724233]\n",
+      "J= [4.51709728]\n",
+      "J= [4.51695275]\n",
+      "J= [4.51680874]\n",
+      "J= [4.51666525]\n",
+      "J= [4.51652227]\n",
+      "J= [4.51637981]\n",
+      "J= [4.51623786]\n",
+      "J= [4.51609643]\n",
+      "J= [4.5159555]\n",
+      "Maximum iterations exceeded!\n",
+      "theta0=[-3.24140214]theta1=[1.1272942]\n"
+     ]
+    },
+    {
+     "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": [
+    "#Computing cost function\n",
+    "def cost_function(m,theta0,theta1,x,y):\n",
+    "    return 1/2/m* sum([(theta0 + theta1*np.asarray([x[i]])-y[i])**2 for i in range(m)])      # Here m is the number of training exaples, theta0 and theta1 are the parameters\n",
+    "                                                                                                # theta0+theta1*X is our hypotheses function \n",
+    "    \n",
+    "#Gradient Descent Algorithm function\n",
+    "def gradient_descent(alpha,x,y,precion_rate=0.0001,max_iterations=1000):\n",
+    "    converged=False\n",
+    "    iterations=0\n",
+    "    m=x.shape[0]         #number of training samples\n",
+    "    \n",
+    "    #initializing theta\n",
+    "    theta0=0\n",
+    "    theta1=0\n",
+    "    \n",
+    "    #cost function J(theta) for mean squared error\n",
+    "    J = cost_function(m,theta0,theta1,x,y)\n",
+    "    print('J=',J)\n",
+    "    \n",
+    "    #Iterate loop\n",
+    "    num_iterations=0\n",
+    "    while not converged:\n",
+    "        # for each training we will compute the gradient (d/d_theta J(theta))\n",
+    "        grad0= 1.0/m*sum([(theta0 + theta1*np.asarray([x[i]])-y[i]) for i in range (m)])\n",
+    "        grad1= 1.0/m*sum([(theta0 + theta1*np.asarray([x[i]])-y[i])*np.asarray([x[i]]) for i in range(m)])\n",
+    "        \n",
+    "        #update the temporary parameters \n",
+    "        temp0= theta0 - alpha*grad0\n",
+    "        temp1= theta1 - alpha*grad1\n",
+    "        \n",
+    "        #update actual parameters\n",
+    "        theta0=temp0\n",
+    "        theta1=temp1\n",
+    "        \n",
+    "        #mean squared error \n",
+    "        e = cost_function(m,theta0,theta1,x,y)\n",
+    "        print('J=',e)\n",
+    "        J=e             #update error\n",
+    "        iterations+=1   #update iterations\n",
+    "        \n",
+    "        \n",
+    "        if iterations== max_iterations:\n",
+    "            print(\"Maximum iterations exceeded!\")\n",
+    "            converged=True\n",
+    "        \n",
+    "    return theta0,theta1\n",
+    "    \n",
+    "\n",
+    "if __name__== '__main__':\n",
+    "    df=pd.read_csv('file1.txt',names=['x','y'])                           #the file has been added to the repository\n",
+    "    x=df['x']\n",
+    "    y=df['y']\n",
+    "    \n",
+    "    alpha=0.01  #learning rate\n",
+    "    precision_rate=0.01     #convergence criteria \n",
+    "    \n",
+    "    #call gradient descent, and get the values for intercept(=theta0) and slope(=theta1) according to the equation y=m*x+c\n",
+    "    theta0,theta1= gradient_descent(alpha,x,y,precision_rate,max_iterations=1000)\n",
+    "    print('theta0='+str(theta0)+ 'theta1='+str(theta1))\n",
+    "    \n",
+    "    #plot to evaluate perfromance\n",
+    "    for i in range (x.shape[0]):\n",
+    "        y_predict=theta0+theta1*x\n",
+    "    \n",
+    "    pylab.plot(x,y,'o')\n",
+    "    pylab.plot(x,y_predict,'k-')\n",
+    "    pylab.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": "3.6.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

From b94341d4c704a463c653e06be886ef477849f028 Mon Sep 17 00:00:00 2001
From: Taru <32308101+epicalyx@users.noreply.github.com>
Date: Mon, 8 Oct 2018 23:32:42 +0530
Subject: [PATCH 2/2] Normal equation for linear regression

Added implementation for normal equation for linear regression in python and the dataset file.
---
 linear_regression_class/file1.txt          | 97 ++++++++++++++++++++++
 linear_regression_class/normal_equation.py | 41 +++++++++
 2 files changed, 138 insertions(+)
 create mode 100644 linear_regression_class/file1.txt
 create mode 100644 linear_regression_class/normal_equation.py

diff --git a/linear_regression_class/file1.txt b/linear_regression_class/file1.txt
new file mode 100644
index 00000000..24cba746
--- /dev/null
+++ b/linear_regression_class/file1.txt
@@ -0,0 +1,97 @@
+6.1101,17.592
+5.5277,9.1302
+8.5186,13.662
+7.0032,11.854
+5.8598,6.8233
+8.3829,11.886
+7.4764,4.3483
+8.5781,12
+6.4862,6.5987
+5.0546,3.8166
+5.7107,3.2522
+14.164,15.505
+5.734,3.1551
+8.4084,7.2258
+5.6407,0.71618
+5.3794,3.5129
+6.3654,5.3048
+5.1301,0.56077
+6.4296,3.6518
+7.0708,5.3893
+6.1891,3.1386
+20.27,21.767
+5.4901,4.263
+6.3261,5.1875
+5.5649,3.0825
+18.945,22.638
+12.828,13.501
+10.957,7.0467
+13.176,14.692
+22.203,24.147
+5.2524,-1.22
+6.5894,5.9966
+9.2482,12.134
+5.8918,1.8495
+8.2111,6.5426
+7.9334,4.5623
+8.0959,4.1164
+5.6063,3.3928
+12.836,10.117
+6.3534,5.4974
+5.4069,0.55657
+6.8825,3.9115
+11.708,5.3854
+5.7737,2.4406
+7.8247,6.7318
+7.0931,1.0463
+5.0702,5.1337
+5.8014,1.844
+11.7,8.0043
+5.5416,1.0179
+7.5402,6.7504
+5.3077,1.8396
+7.4239,4.2885
+7.6031,4.9981
+6.3328,1.4233
+6.3589,-1.4211
+6.2742,2.4756
+5.6397,4.6042
+9.3102,3.9624
+9.4536,5.4141
+8.8254,5.1694
+5.1793,-0.74279
+21.279,17.929
+14.908,12.054
+18.959,17.054
+7.2182,4.8852
+8.2951,5.7442
+10.236,7.7754
+5.4994,1.0173
+20.341,20.992
+10.136,6.6799
+7.3345,4.0259
+6.0062,1.2784
+7.2259,3.3411
+5.0269,-2.6807
+6.5479,0.29678
+7.5386,3.8845
+5.0365,5.7014
+10.274,6.7526
+5.1077,2.0576
+5.7292,0.47953
+5.1884,0.20421
+6.3557,0.67861
+9.7687,7.5435
+6.5159,5.3436
+8.5172,4.2415
+9.1802,6.7981
+6.002,0.92695
+5.5204,0.152
+5.0594,2.8214
+5.7077,1.8451
+7.6366,4.2959
+5.8707,7.2029
+5.3054,1.9869
+8.2934,0.14454
+13.394,9.0551
+5.4369,0.61705
\ No newline at end of file
diff --git a/linear_regression_class/normal_equation.py b/linear_regression_class/normal_equation.py
new file mode 100644
index 00000000..168cf065
--- /dev/null
+++ b/linear_regression_class/normal_equation.py
@@ -0,0 +1,41 @@
+#!/usr/bin/env python
+# coding: utf-8
+
+# In[42]:
+
+
+#Importing all the required libraries
+import pandas as pd
+import matplotlib.pyplot as plt
+import pylab
+import numpy as np
+from numpy.linalg import inv
+import random
+
+
+# In[45]:
+
+
+''' According to normal equation method the optimal value of parameter theta for which cost function is minimum can be computed by 
+ setting the derivative of cost function with respect to each value of theta in the parameter matrix to 0
+ By this method we get the parameter matrix theta equal to:
+ theta = inverse(X'*X)*X'*Y   , where X' = transpose of X(feature matrix) and where  Y is the target matrix'''
+if __name__== '__main__':
+    df=pd.read_csv('file1.txt',names=['x','y'])                     #the file has been added to the repository
+    x=df['x']
+    y=df['y']
+    m=x.shape[0]                                                    #no. of training examples
+    X=[np.array([x[i]])for i in range (m)]                          #converting the table of input features into a matrix
+    Y=[np.array([y[i]]) for i in range (m)]                         #converting the target features values into a matrix
+    Xtrans=np.transpose(X)
+    theta_best=np.dot((np.dot((inv(np.dot(Xtrans,X))),Xtrans)),y)   #computing the value of theta for which cost function is minimum by using the normal equation
+    
+    
+    #plot to evaluate perfromance
+    for i in range (x.shape[0]):
+        y_predict=theta_best*X
+    
+    pylab.plot(x,y,'o')
+    pylab.plot(x,y_predict,'k-')
+    pylab.show()
+