Machine learning吴恩达第三周 Logistic Regression
1. Sigmoid function
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
2. Logistic Regression Cost & Logistic Regression Gradient
首先可以将h(x)表示出来----sigmoid函数
然后对于gredient(j)来说,
可以现在草稿纸上把矩阵画出来,然后观察,用向量来解决;
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);
for i=1:m,
J=J+1/m*(-y(i)*log(h(i))-(1-y(i))*log(1-h(i)));
endfor
grad=1/m*X'*(h.-y);
% =============================================================
end
3. Predict
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);
for i=1:m
if(p(i)>=0.5)p(i)=1;
else p(i)=0;
end
endfor
% =========================================================================
end
4.Regularized Logistic Regression Cost & Regularized Logistic Regression Gradient
要注意的是:
Octave中,下标是从1开始的;
其次:
对于gradient(j)而言;
我们可以用X(:,j)的方式获取第j列的所有元素;
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);
for i=1:m
J=J+1/m*(-y(i)*log(h(i))-(1-y(i))*log(1-h(i)));
endfor
for i=2:length(theta)
J=J+lambda/(2*m)*theta(i)^2;
endfor
grad(1)=1/m*(h-y)'*X(:,1);
for i=2:length(theta)
grad(i)=1/m*(h-y)'*X(:,i)+lambda/m*theta(i);
endfor
% =============================================================
end