逻辑回归，梯度下降 Octave 实现

Question

我正在学习 Ng 教授的机器学习课程。 有一个作业需要实现逻辑回归梯度下降。 这是我的代码：

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
[~,n] = size(X);
% 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 = ((-y'*log(sigmoid(X*theta)))-((1-y)'*log(1-sigmoid(X*theta))))/m;
for j = 1:n
  temp_sum = 0;
  for i = 1:m
    temp_sum+=(sigmoid(X(i,:)*theta)-y(i))*X(i,j);
  endfor
  grad(j) = theta(j)-temp_sum;
endfor

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

end

这是我试图实现的公式：

其中 x 的 h 代表 sigmoid 函数。 我检查了 sigmoid 函数是否正确，但我仍然无法理解该算法的错误之处。 如果您发现任何问题，请告诉我。

Answer 1

我相信你也应该得到梯度的平均值grad = grad / m，就像成本J一样。但是自从我上次上 Andrew Ng 的课程以来已经有一段时间了，所以我可能错了。

Answer 2

试试这个..这就是我为我的任务所做的。我认为你错过了 m 的除法。

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);
t1=(y'*log(h));
t2=(1-y)'*log(1-h);
J=-(t1+t2)/m;

for i =1:length(theta)
grad(i)=((h-y)'*X(:,i))/m;
endfor

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

end