Coursera吴恩达机器学习编程作业（ex2）正则化的LogisticRegression

最新推荐文章于 2021-05-23 00:45:51 发布

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本文详细介绍了Logistic回归算法的实现过程，包括Sigmoid函数计算、代价函数计算、梯度计算及正则化处理等内容，并提供了预测函数的具体实现。

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实现函数：

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).
A=-1*z;
B=exp(A)+1;
g=1./B;
% =============================================================

end

计算代价函数以及

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));

% ====================== 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);%hypothesis function
A=-1*y'*log(h);
B=(1.-y)'*log(1.-h);
J=1/m*sum(A-B);%cost

grad=1/m*(X'*(h-y));%derivative of theta


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

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:m
  if(h(i)<0.5)
  p(i)=0;
  else
  p(i)=1;
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);
A=-1*y'*log(h);
B=(1.-y)'*log(1.-h);
thetao=theta;
thetao(1,1)=0;
C=thetao.^2;
J=1/m*sum(A-B)+lambda/(2*m)*sum(C);%cost

grad=1/m*(X'*(h-y));
d=grad(1);
grad=grad+lambda/m*theta;
grad(1)=d;
% =============================================================

end