My solutions to Exercises for Week 3 : Regularization - Logistic Regression (Coursera.org - Machine Learning Course):

1. Sigmoid Function

function g = sigmoid(z) %SIGMOID Compute sigmoid functoon % J = SIGMOID(z) computes the sigmoid of z. % You need to return the following variables correctly g = zeros(size(z)); % ====================== YOUR CODE HERE ====================== % Instructions: Compute the sigmoid of each value of z (z can be a matrix, % vector or scalar). for i = 1:size(z, 1) for j=1:size(z, 2) g(i, j) = pinv(1+pinv(e^z(i, j))); end end % ============================================================= end

2. Compute cost for logistic regression

function [J, grad] = costFunction(theta, X, y) %COSTFUNCTION Compute cost and gradient for logistic regression % J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the % parameter for logistic regression and the gradient of the cost % w.r.t. to the parameters. % Initialize some useful values m = length(y); % number of training examples % You need to return the following variables correctly J = 0; grad = zeros(size(theta)); % ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta. % You should set J to the cost. % Compute the partial derivatives and set grad to the partial % derivatives of the cost w.r.t. each parameter in theta % % Note: grad should have the same dimensions as theta % thetaTx = (theta'*X')'; h = sigmoid(thetaTx); J = -(1/m)*(sum(y'*log(h)+(1-y)'*log(1-h))); grad = (1/m)*(((h-y)'*X)'); % ============================================================= end

3. Gradient for logistic regression

4. Predict Function

function p = predict(theta, X) %PREDICT Predict whether the label is 0 or 1 using learned logistic %regression parameters theta % p = PREDICT(theta, X) computes the predictions for X using a % threshold at 0.5 (i.e., if sigmoid(theta'*x) >= 0.5, predict 1) m = size(X, 1); % Number of training examples % You need to return the following variables correctly p = zeros(m, 1); % ====================== YOUR CODE HERE ====================== % Instructions: Complete the following code to make predictions using % your learned logistic regression parameters. % You should set p to a vector of 0's and 1's % thetaTx = (theta'*X')'; h = sigmoid(thetaTx); for i = 1:m if h(i)>=0.5 p(i) = 1; else p(i) = 0; end end % ========================================================================= end

5. Compute cost for regularized LR

function [J, grad] = costFunctionReg(theta, X, y, lambda) %COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization % J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using % theta as the parameter for regularized logistic regression and the % gradient of the cost w.r.t. to the parameters. % Initialize some useful values m = length(y); % number of training examples % You need to return the following variables correctly J = 0; grad = zeros(size(theta)); % ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta. % You should set J to the cost. % Compute the partial derivatives and set grad to the partial % derivatives of the cost w.r.t. each parameter in theta thetaTx = (theta'*X')'; h = sigmoid(thetaTx); leftJ = -(1/m)*(sum(y'*log(h)+(1-y)'*log(1-h))); rightJ = (lambda/(2*m))*sum((theta.^2)(2:end,1)); J = leftJ+rightJ; error = h-y; grad(1) = (error'*X(:,1))/m ; for i=2:size(grad, 1) grad(i) = (error'*X(:,i) + (lambda*theta(i)))/m; end % ============================================================= end

6. Gradient for regularized LR

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