注意:X是一个m*(n+1)的矩阵,矩阵的第一列都是1!,\theta是一个(n+1)*1的向量,保存的是我们要预测的参数值

第一题:sigmoid函数
输入一个矩阵,返回每一个元素做计算的值

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./(ones(size(z))+exp(-z))
% ============================================================
end

第二题:不正则化的梯度迭代:
返回

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);
J = (-log(h.')*y - log(ones(1, m) - h.')*(ones(m, 1) - y)) / m;
grad = (X.' * (h - y)) /m;
% ============================================================

end

首先先求出预测值,就用第一题的那个函数,求出预测值(注意:X*theta是第一个实验作业里面的线性回归函数的表达式)注意:h.就是求转置的意思,这样可以带入代价函数算出J
grad就是每一次下降的时候递减的值,注意:没算学习效率

第三题:0&1判断
这时候就用一手if对矩阵每个元素进行判定
像exp,log,if这些作用在矩阵里面就是对每个元素求值

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);
p = (h >= 0.5);
% ============================================================
end

第四题:有正则化的代价函数求值:

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);
J = (-log(h.')*y - log(ones(1, m) - h.')*(ones(m, 1) - y)) / m +(lambda/(2*m)) * sum(theta(2:end).^2);
grad(1) = (X(:, 1).' * (h - y)) /m;
grad(2:end) = (X(:, 2:end).' * (h - y)) /m + (lambda/m) * theta(2:end);
% ============================================================

end

这里主要区分了grad中1和2之间的区别,其他的和公式相差无二

最后修改日期:2020年11月2日