斯坦福大学-多元线性回归_Exercise Code

Multivariate Linear Regression 多元线性回归

http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex3/ex3.html

clear all; close all; clcx = load('ex3x.dat'); y = load('ex3y.dat');m = length(y);% Add intercept term to xx = [ones(m, 1), x];% Save a copy of the unscaled features for laterx_unscaled = x;% Scale features and set them to zero meanmu = mean(x);sigma = std(x);x(:,2) = (x(:,2) - mu(2))./ sigma(2);x(:,3) = (x(:,3) - mu(3))./ sigma(3);% Prepare for plottingfigure;% plot each alpha's data points in a different style% braces indicate a cell, not just a regular array.plotstyle = {'b', 'r', 'g', 'k', 'b--', 'r--'};% Gradient Descent alpha = [0.01, 0.03, 0.1, 0.3, 1, 1.3];MAX_ITR = 100;% this will contain my final values of theta% after I've found the best learning ratetheta_grad_descent = zeros(size(x(1,:))); for i = 1:length(alpha)    theta = zeros(size(x(1,:)))'; % initialize fitting parameters    J = zeros(MAX_ITR, 1);    for num_iterations = 1:MAX_ITR        % Calculate the J term        J(num_iterations) = (0.5/m) .* (x * theta - y)' * (x * theta - y);                % The gradient        grad = (1/m) .* x' * ((x * theta) - y);                % Here is the actual update        theta = theta - alpha(i) .* grad;    end    % Now plot the first 50 J terms    plot(0:49, J(1:50), char(plotstyle(i)), 'LineWidth', 2)    hold on        % After some trial and error, I find alpha=1    % is the best learning rate and converges    % before the 100th iteration    %    % so I save the theta for alpha=1 as the result of     % gradient descent    if (alpha(i) == 1)        theta_grad_descent = theta;    endendlegend('0.01','0.03','0.1', '0.3', '1', '1.3')xlabel('Number of iterations')ylabel('Cost J')% force Matlab to display more than 4 decimal places% formatting persists for rest of this sessionformat long% Display gradient descent's resulttheta_grad_descent% Estimate the price of a 1650 sq-ft, 3 br houseprice_grad_desc = dot(theta_grad_descent, [1, (1650 - mu(2))/sigma(2),...                    (3 - mu(3))/sigma(3)])% Calculate the parameters from the normal equationtheta_normal = (x_unscaled' * x_unscaled)\x_unscaled' * y%Estimate the house price againprice_normal = dot(theta_normal, [1, 1650, 3])