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POLinear Regression with Multiple Variables - Python - Implementation issues
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copied!<p>I am trying to implement Linear Regression with Multiple variables( actually , just 2 ) . I am using the data from the ML-Class Stanford. I got it working correctly for the single variable case. The same code <em>should</em> have worked for multiple, but , does not. </p> <p>LINK to the data : </p> <p><a href="http://s3.amazonaws.com/mlclass-resources/exercises/mlclass-ex1.zip" rel="nofollow" title="DATA">http://s3.amazonaws.com/mlclass-resources/exercises/mlclass-ex1.zip</a></p> <p>Feature Normalization:</p> <pre><code>''' This is for the regression with multiple variables problem . You have to normalize features before doing anything. Lets get started''' from __future__ import division import os,sys from math import * def mean(f,col): #This is to find the mean of a feature sigma = 0 count = 0 data = open(f,'r') for line in data: points = line.split(",") sigma = sigma + float(points[col].strip("\n")) count+=1 data.close() return sigma/count def size(f): count = 0 data = open(f,'r') for line in data: count +=1 data.close() return count def standard_dev(f,col): #Calculate the standard_dev . Formula : Sqrt ( Sigma ( x - x') ** (x-x') ) / N ) data = open(f,'r') sigma = 0 mean = 0 if(col==0): mean = mean_area else: mean = mean_bedroom for line in data: points = line.split(",") sigma = sigma + (float(points[col].strip("\n")) - mean) ** 2 data.close() return sqrt(sigma/SIZE) def substitute(f,fnew): ''' Take the old file. 1. Subtract the mean values from each feature 2. Scale it by dividing with the SD ''' data = open(f,'r') data_new = open(fnew,'w') for line in data: points = line.split(",") new_area = (float(points[0]) - mean_area ) / sd_area new_bedroom = (float(points[1].strip("\n")) - mean_bedroom) / sd_bedroom data_new.write("1,"+str(new_area)+ ","+str(new_bedroom)+","+str(points[2].strip("\n"))+"\n") data.close() data_new.close() global mean_area global mean_bedroom mean_bedroom = mean(sys.argv[1],1) mean_area = mean(sys.argv[1],0) print 'Mean number of bedrooms',mean_bedroom print 'Mean area',mean_area global SIZE SIZE = size(sys.argv[1]) global sd_area global sd_bedroom sd_area = standard_dev(sys.argv[1],0) sd_bedroom=standard_dev(sys.argv[1],1) substitute(sys.argv[1],sys.argv[2]) </code></pre> <p>I have implemented mean and Standard deviation in the code, instead of using NumPy/SciPy. After storing the values in a file , a snapshot of which is the following:</p> <p><strong><code>X1 X2 X3 COST OF HOUSE</code></strong></p> <pre><code>1,0.131415422021,-0.226093367578,399900 1,-0.509640697591,-0.226093367578,329900 1,0.507908698618,-0.226093367578,369000 1,-0.743677058719,-1.5543919021,232000 1,1.27107074578,1.10220516694,539900 1,-0.0199450506651,1.10220516694,299900 1,-0.593588522778,-0.226093367578,314900 1,-0.729685754521,-0.226093367578,198999 1,-0.789466781548,-0.226093367578,212000 1,-0.644465992588,-0.226093367578,242500 </code></pre> <p>I run regression on it to find the parameters. The code for that is below:</p> <pre><code>''' The plan is to rewrite and this time, calculate cost each time to ensure its reducing. Also make it enough to handle multiple variables ''' from __future__ import division import os,sys def computecost(X,Y,theta): #X is the feature vector, Y is the predicted variable h_theta=calculatehTheta(X,theta) delta = (h_theta - Y) * (h_theta - Y) return (1/194) * delta def allCost(f,no_features): theta=[0,0] sigma=0 data = open(f,'r') for line in data: X=[] Y=0 points=line.split(",") for i in range(no_features): X.append(float(points[i])) Y=float(points[no_features].strip("\n")) sigma=sigma+computecost(X,Y,theta) return sigma def calculatehTheta(points,theta): #This takes a file which has (1,feature1,feature2,so ... on) #print 'Points are',points sigma = 0 for i in range(len(theta)): sigma = sigma + theta[i] * float(points[i]) return sigma def gradient_Descent(f,no_iters,no_features,theta): ''' Calculate ( h(x) - y ) * xj(i) . And then subtract it from thetaj . Continue for 1500 iterations and you will have your answer''' X=[] Y=0 sigma=0 alpha=0.01 for i in range(no_iters): for j in range(len(theta)): data = open(f,'r') for line in data: points=line.split(",") for i in range(no_features): X.append(float(points[i])) Y=float(points[no_features].strip("\n")) h_theta = calculatehTheta(points,theta) delta = h_theta - Y sigma = sigma + delta * float(points[j]) data.close() theta[j] = theta[j] - (alpha/97) * sigma sigma = 0 print theta print allCost(sys.argv[1],2) print gradient_Descent(sys.argv[1],1500,2,[0,0,0]) </code></pre> <p>It prints the following as the parameters:</p> <p>[-3.8697149722857996e-14, 0.02030369056348706, 0.979706406501678]</p> <p>All three are horribly wrong :( The exact same thing works with Single variable . </p> <p>Thanks !</p>

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