吴恩达的机器学习编程作业 2.gradientDescent 线性回归迭代计算代价函数及特征变量

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本文详细介绍了梯度下降算法的基本原理及其实现过程。通过具体的MATLAB代码示例，读者可以了解到如何利用梯度下降法来更新参数θ，以最小化代价函数。文中还涉及了学习率α的选择以及迭代次数对算法效果的影响。

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
%GRADIENTDESCENT Performs gradient descent to learn theta
%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
%   taking num_iters gradient steps with learning rate alpha

% Initialize some useful values
m = length(y); % number of training examples
J_history = zeros(num_iters, 1);

for iter = 1:num_iters

    % ====================== YOUR CODE HERE ======================
    % Instructions: Perform a single gradient step on the parameter vector
    %               theta. 
    %
    % Hint: While debugging, it can be useful to print out the values
    %       of the cost function (computeCost) and gradient here.
    %
	n = X' * (X*theta - y)
	size(n)
	theta = theta - alpha/m * n;
    % ============================================================
    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);

end

end