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,X(neg,'ko','MarkerFaceColor','y',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,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,y,lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
% J = COSTFUNCTIONREG(theta,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