coursera machine-learning-ex2 课程作业记录
最近在学习 coursera 上 吴恩达 的机器学习课程，记录一下作业答案。
Logistic Regression
function g = sigmoid(z) %SIGMOID Compute sigmoid function % g = SIGMOID(z) computes the sigmoid of z.% You need to return the following variables correctly
% ====================== 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
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(Xtheta))-(1-y)’log(1-sigmoid(Xtheta)));
grad=1/mX’(sigmoid(X*theta)-y);% =============================================================
end
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=sigmoid(X*theta)>=0.5;
% =========================================================================
end
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 thetaJ=1/m*(-y’log(sigmoid(Xtheta))-(1-y)’log(1-sigmoid(Xtheta)))+lambda/2/mtheta(2:end)’theta(2:end);
grad=1/mX’(sigmoid(Xtheta)-y)+lambda/mtheta;grad(1)=grad(1)-lambda/m*theta(1);
% =============================================================
end
function out = mapFeature(X1, X2) % MAPFEATURE Feature mapping function to polynomial features % % MAPFEATURE(X1, X2) maps the two input features % to quadratic features used in the regularization exercise. % % Returns a new feature array with more features, comprising of % X1, X2, X1.^2, X2.^2, X1*X2, X1*X2.^2, etc.. % % Inputs X1, X2 must be the same size %degree = 6;
out = ones(size(X1(:,1)));
for i = 1:degree
for j = 0:i
out(:, end+1) = (X1.^(i-j)).*(X2.^j);
end
endend