Coursera机器学习课程笔记（三）

记录作业的解答

1.Sigmoid Function

sigmoid.m文件：

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).

[m,n] = size(z);

for i = 1:m
    for j = 1:n
        g(i,j) = 1 / (1 + exp(-z(i,j)));
    end
end

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

end

2.Logistic Regression Cost

与3同时完成，都在costFunction.m文件内

3.Logistic Regression Gradient

costFunction.m文件：

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) * (-y' * log(sigmoid(X * theta)) - (1-y)' * log(1 - sigmoid(X * theta)));

for j = 1:length(theta)
    grad(j) = (1/m) * X(:,j)' * (sigmoid(X * theta) - y);
end
% =============================================================

end

4.Predict

predict.m文件：

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
%

for i = 1:m
    if sigmoid(X(i,:) * theta) >= 0.5
        p(i) = 1;
    else
        p(i) = 0;
    end
end
% =========================================================================
end

5.Regularized Logistic Regression Cost

与6同时完成，都在costFunctionReg.m文件内

6.Regularized Logistic Regression Gradient

costFunctionReg.m文件：

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

sum = 0;
%根据公式，注意theta(1)不参与计算
for j = 2:length(theta)
    sum = sum + theta(j) ^ 2;
end
J = (1/m) * (-y' * log(sigmoid(X * theta)) - (1-y)' * log(1 - sigmoid(X * theta))) + lambda/(2*m) * sum;

%根据公式，注意grad(1)不用考虑正则化
grad(1) = (1/m) * X(:,1)' * (sigmoid(X * theta) - y);
for j = 2:length(theta)
    grad(j) = (1/m) * X(:,j)' * (sigmoid(X * theta) - y) + lambda/m * theta(j) ;
end


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

end