Question: Regularization can be added to gradient descent by modifying the theta update step from: tempj=jn1i=1n(h(,x(i))y(i))(x(i)) To: tempj=jn{[i=1n(h(,x(i))y(i))(x(i))]+[j]} Copy gradientDescentMulti.m from Hwk2 to gradientDescentMultiReg.m. Update gradientDescentMultiReg.m

 Regularization can be added to gradient descent by modifying the theta

Regularization can be added to gradient descent by modifying the theta update step from: tempj=jn1i=1n(h(,x(i))y(i))(x(i)) To: tempj=jn{[i=1n(h(,x(i))y(i))(x(i))]+[j]} Copy gradientDescentMulti.m from Hwk2 to gradientDescentMultiReg.m. Update gradientDescentMultiReg.m such that it includes the above update step (Note- do not update how you calculate the bias term 0, do not change how you calculate temp 0 ) and calls computeCostReg.m from the problem 9. Use the following matlab code: clear ; close all; data = load('...'hwk2lex1data1.txt'); \% Dataset from Andrew Ng, Machine Learning MOOC X=data(:,1); y=data(:,2) M=[ ones ( length (X),1)X]; theta init = zeros(2,1); \% initialize fitting parameters to zero % Some gradient descent settings iterations =1500; alpha =0.01; lambda =0; % run gradient descent theta unreg = gradientDescentMultiReg(M, y, theta init, alpha, iterations,lambda); lin_reg =((MM)\M)y;% optimal solution lambda =1; theta_reg = gradientDescentMultiReg(M, y, theta init, alpha, iterations,lambda); fprintf('Linear Regression: [\%f, \%f] \ ',lin_reg); fprintf('Gradient Descent: [\%f,\%f]ln',theta unreg); fprintf('Regularized Gradient Descent: [\%f, %f] ',theta_reg); Do not continue until you get: Linear Regression: [3.895781,1.193034] Gradient Descent: [3.630291,1.166362] Regularized Gradient Descent: [-3.624388,1.165623] Change lambda =100, what are the new regularized gradient descent weights? Ans (show gradientDescentMultiReg.m code and ans with lambda=100)

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