第八章节编程作业：Logistic Regression

需要自己编程的主要包括以下5个文件：

plotData.m
sigmoid.m
costFunction.m
predict.m
costFunctionReg.m

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.

% 找到所有正（1）负（0）对应的坐标（行号）
pos = find(y==1); neg = find(y==0);
% 画图
% k+为黑色的+符号；LineWidth线粗，MarkerSize为大小；
plot(X(pos,1),X(pos,2),'k+','LineWidth',2,'MarkerSize',7);
% ko为黑色的圆o；MarkerFaceColor，y,内部填充为黄色；
plot(X(neg,1),X(neg,2),'ko','MarkerFaceColor','y','MarkerSize',7);

% =================================================
hold off;

end

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));      %初始化g

% ====================== 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));
% 当z = 0时,g = 0.5;z趋于正无穷时，g趋于1，z趋于负无穷时，g趋于0；
% =============================================================

end

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));  %grad与theta纬数一致

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

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

end

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

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

h = sigmoid(X*theta);
theta(1) = 0;
% J = sum(-y'*log(h)-(1-y')*log(1-h))/m+lambda/(2*m)*sum(power(theta,2));
J = (-y'*log(h)-(1-y')*log(1-h))/m+lambda/(2*m)*(theta')*theta;
% 如果是标量，则sum可以省略；如果是矩阵（有维度），则不可以省略
grad = ((h-y)'*X)/m+lambda/m*theta';
% theta0不参与正则化，而matlab中下标从1开始，所以theta(1)=theta0;
% 这样theta0的偏导为 grad = ((h-y)'*X)/m
% =============================================================

end