Andrew Ng机器学习week3(Regularization)编程习题

Andrew Ng机器学习week3(Regularization)编程习题

1、plotData.m

function plotData(X, y) %PLOTDATA Plots the data points X and y into a new figure % PLOTDATA(x,y) plots the data points with + for the positive examples % and o for the negative examples. X is assumed to be a Mx2 matrix. % Create New Figure figure; hold on; % ====================== YOUR CODE HERE ====================== % Instructions: Plot the positive and negative examples on a % 2D plot, using the option 'k+' for the positive % examples and 'ko' for the negative examples. % pos = find(y == 1); neg = find(y == 0); plot(X(pos, 1), X(pos, 2), 'k+', 'LineWidth', 2, 'MarkerSize', 7); plot(X(neg, 1), X(neg, 2), 'ko', 'MarkerFaceColor', 'y', 'MarkerSize', 7); % ========================================================================= hold off; end

2、sigmoid.m

function g = sigmoid(z) %SIGMOID Compute sigmoid function % g = 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). g = 1 ./ (1 + exp(-z)) % ============================================================= end

3、costFunction.m

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 % J = ((-y' * log(sigmoid(X * theta))) - (1 - y)' * log(1 - sigmoid(X * theta))) / m; grad = (X' * (sigmoid(X * theta) - y)) ./ m; % ============================================================= end

4、predict.m

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 % p = floor(sigmoid(X * theta) .* 2) % ========================================================================= end

5、costFunctionReg.m

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 J = ((-y' * log(sigmoid(X * theta))) - (1 - y)' * log(1 - sigmoid(X * theta))) / m + (sum(theta .^ 2) - theta(1) ^ 2) * lambda / (2 * m); grad(1) = (X(:, 1)' * (sigmoid(X * theta) - y)) ./ m; for i = 2 : size(theta) grad(i) = (X(:, i)' * (sigmoid(X * theta) - y)) ./ m + lambda * theta(i) / m % ============================================================= end