Coursera machine learning 第二周 编程作业 Linear Regression
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必做：
[*] warmUpExercise.m - Simple example function in Octave/MATLAB
[*] plotData.m - Function to display the dataset
[*] computeCost.m - Function to compute the cost of linear regression
[*] gradientDescent.m - Function to run gradient descent
1.warmUpExercise.m
A = eye(5);
2.plotData.m
plot(x, y, ‘rx‘, ‘MarkerSize‘, 10); % Plot the data ylabel(‘Profit in $10,000s‘); % Set the y-axis label xlabel(‘Population of City in 10,000s‘); % Set the x-axis label
3.computeCost.m
function J = computeCost(X, y, theta) %COMPUTECOST Compute cost for linear regression % J = COMPUTECOST(X, y, theta) computes the cost of using theta as the % parameter for linear regression to fit the data points in X and y % Initialize some useful values m = length(y); % number of training examples % You need to return the following variables correctly J = 0; % ====================== YOUR CODE HERE ====================== % Instructions: Compute the cost of a particular choice of theta % You should set J to the cost.H = X*theta-y; J = (1/(2*m))*sum(H.*H); % ========================================================================= end
公式： 
注意matlab中 .* 的用法。
4.gradientDescent.m
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. H = X*theta-y;
theta(1)=theta(1)-alpha*(1/m)*sum(H.*X(:,1));
theta(2)=theta(2)-alpha*(1/m)*sum(H.*X(:,2));% ============================================================ % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta); end end
单变量梯度下降
对函数J(θ)求偏导
即 H.*X(:,1)
θi向着梯度最小的方向减少,alpha为步长。
theta(i)=theta(i)-alpha*(1/m)*sum(H.*X(:,i));
原文：http://www.cnblogs.com/smartweed/p/6784161.html
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