machine-learning - 我的梯度下降没有给出确切的值

Question

我已经在Octave中编写了梯度下降 算法，但它并没有给我确切的答案。答案从一位数到两位数不等。

这是我的代码：

function theta = gradientDescent(X, y, theta, alpha, num_iters)

m = length(y); % number of training examples
s = 0;
temp = theta;
for iter = 1:num_iters
  for j = 1:size(theta, 1)
    for i = 1:m
      h = theta' * X(i, :)';
      s = s + (h - y(i))*X(i, j);
    end
    s = s/m;
    temp(j) = temp(j) - alpha * s;
  end 
  theta = temp; 
end

end

为了：

theta = gradientDescent([1 5; 1 2; 1 4; 1 5],[1 6 4 2]',[0 0]',0.01,1000);

我的梯度下降给出了这个：

 4.93708
-0.50549

但预计会给出这个：

 5.2148
-0.5733

Answer 1

小修复：

1. 您的变量s可能增量初始化不正确。
2. 所以它的temp变量可能是new theta
3. 错误地计算增量

尝试以下更改。

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)

m = length(y); % number of training examples
J_history = zeros(num_iters, 1);
temp = theta;
for iter = 1:num_iters
    temp = zeros(length(theta), 1);
    for j = 1:size(theta)
        s = 0
        for i = 1:m
            s = s + (X(i, :)*theta - y(i)) * X(i, j);
        end
    end
    s = s/m;
    temp(j) = temp(j) - alpha * s;
end 
    theta = temp; 
    J_history(iter) = computeCost(X, y, theta);
end
end