Machine Learning - Week3 Logistic Regression ex2

sigmoid函数:

function g = sigmoid(z)

g = zeros(size(z));

g = 1 ./ (1 + exp(-z));

end

cost和gradient函数： 直接用向量化公式

function [J, grad] = costFunction(theta, X, y)

m = length(y);

J = 0;

grad = zeros(size(theta));

% h size: m * 1

h = sigmoid(X * theta);

% y' * log(h) size: 1 * 1

J = -1 / m * (y' * log(h) + (1 - y)' * log (1 - h));

% X' size: (n+1) * m, X*theta size: m * 1, grad size: (n+1) * 1

grad = (X' * (sigmoid(X * theta) - y)) / m;

end

predict函数： 注意使用find()直接按条件批量处理

function p = predict(theta, X)

m = size(X, 1);

p = zeros(m, 1);

positiveIdx = find(sigmoid(X * theta) >= 0.5);

p(positiveIdx) = 1;

end

带Regulation的cost和gradient函数：直接使用向量化公式和切片计算， 注意分别计算grad(1)和grad(2:n+1)

function [J, grad] = costFunctionReg(theta, X, y, lambda)

m = length(y);

J = 0;

grad = zeros(size(theta));

n1 = length(theta);

% h size: m * 1

h = sigmoid(X * theta);

% regularization

bias = lambda / (2 * m) * sum((theta .* theta)(2:n1));

% y' * log(h) size: 1 * 1

J = -1 / m * (y' * log(h) + (1 - y)' * log (1 - h)) + bias;

% X size: (m * (n+1), X' size : (n+1) * m, X'(1) size: 1 * m, y size: m + 1

grad(1) = X'(1, :) * (sigmoid(X * theta) - y) / m;

% X'(2:n1) size: (n) * m, X*theta size: m * 1, grad(2:n1) size: (n) * 1

grad(2:n1) = (X'(2:n1, :) * (sigmoid(X * theta) - y)) / m + lambda * theta(2:n1) / m;

end