Coursera机器学习 week3 逻辑回归 编程作业代码

这是Coursera上 Week3 的 “逻辑回归” 的编程作业代码。经过测验，全部通过。

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下面是 $sigmoid.m$ 的代码：

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).

g = 1 ./ (1 + exp(-z)); % Ff operator './' is replaced with '/', this expression will calculate the
                        % inverse matrix of (1 + exp(-z)).

% =============================================================

end

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下面是 $costFunction.m$ 的代码：

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

% =============================================================

end

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下面是 $predict.m$ 的代码：

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
%

temp = sigmoid(X * theta);
p = temp > 0.5; % If a element is positive, make it 1, or keep it 0

% =========================================================================

end

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下面是 $costFunctionReg.m$ 的代码：

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, grad] = costFunction(theta,X,y);
J = J  + lambda / (2*m) * (sum(theta.^2) - theta(1)^2); % no need to regularize theta 1
grad = grad + lambda / m * theta;
grad(1) = grad(1) - lambda / m * theta(1); % no need to regularize theta 1

% =============================================================

end