吴恩达机器学习 - 逻辑回归的正则化

题目链接：点击打开链接

先贴笔记

代码：

costFunction.m(求代价和各方向梯度)(注意：$Θ_{0}$单独计算)：

function [J,grad] = costFunctionReg(theta,X,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

[~,n] = size(X);
%以下计算一定要记得不正则化theta_0
J = (-y'*log(sigmoid(X*theta))-(1-y')*log(1-sigmoid(X*theta)))/m + ...
lambda/(2.0*m)*(theta(2:n)'*theta(2:n));

grad(1) = X(:,1)'*(sigmoid(X*theta)-y)./m;
grad(2:n) = X(:,2:n)'*(sigmoid(X*theta)-y)./m + lambda/m*theta(2:n);


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

end

然后展示下不同λ画出的不同图案