%% Machine Learning Online Class - Exercise 1: Linear Regression% Instructions% ------------% % This file contains code that helps you get started on the% linear exercise. You will need to complete the following functions % in this exericse:%% warmUpExercise.m% plotData.m% gradientDescent.m% computeCost.m% gradientDescentMulti.m% computeCostMulti.m% featureNormalize.m% normalEqn.m%% For this exercise, you will not need to change any code in this file,% or any other files other than those mentioned above.%% x refers to the population size in 10,000s% y refers to the profit in $10,000s%%% Initializationclear all; close all; clc%% ==================== Part 1: Basic Function ====================% Complete warmUpExercise.m fprintf('Running warmUpExercise ... \n');fprintf('5x5 Identity Matrix: \n');warmUpExercise()fprintf('Program paused. Press enter to continue.\n');pause;%% ======================= Part 2: Plotting =======================fprintf('Plotting Data ...\n')data = csvread('ex1data1.txt');X = data(:, 1); y = data(:, 2);m = length(y); % number of training examples% Plot Data% Note: You have to complete the code in plotData.mplotData(X, y);fprintf('Program paused. Press enter to continue.\n');pause;%% =================== Part 3: Gradient descent ===================fprintf('Running Gradient Descent ...\n')X = [ones(m, 1), data(:,1)]; % Add a column of ones to x，%前面之所以生成一个1列全为1的列向量是因为要和theta0相乘，否则的话没办法相乘theta = zeros(2, 1); % initialize fitting parameters% Some gradient descent settingsiterations = 1500;alpha = 0.01;% compute and display initial costcomputeCost(X, y, theta)% run gradient descenttheta = gradientDescent(X, y, theta, alpha, iterations);% print theta to screenfprintf('Theta found by gradient descent: ');fprintf('%f %f \n', theta(1), theta(2));% Plot the linear fithold on; % keep previous plot visibleplot(X(:,2), X*theta, '-')legend('Training data', 'Linear regression')hold off % don't overlay any more plots on this figure% Predict values for population sizes of 35,000 and 70,000predict1 = [1, 3.5] *theta;fprintf('For population = 35,000, we predict a profit of %f\n',... predict1*10000);predict2 = [1, 7] * theta;fprintf('For population = 70,000, we predict a profit of %f\n',... predict2*10000);fprintf('Program paused. Press enter to continue.\n');pause;%% ============= Part 4: Visualizing J(theta_0, theta_1) =============fprintf('Visualizing J(theta_0, theta_1) ...\n')% Grid over which we will calculate Jtheta0_vals = linspace(-10, 10, 100);theta1_vals = linspace(-1, 4, 100);% initialize J_vals to a matrix of 0'sJ_vals = zeros(length(theta0_vals), length(theta1_vals));% Fill out J_valsfor i = 1:length(theta0_vals) for j = 1:length(theta1_vals) t = [theta0_vals(i); theta1_vals(j)]; J_vals(i,j) = computeCost(X, y, t); endend% Because of the way meshgrids work in the surf command, we need to % transpose J_vals before calling surf, or else the axes will be flippedJ_vals = J_vals';% Surface plotfigure;surf(theta0_vals, theta1_vals, J_vals)xlabel('\theta_0'); ylabel('\theta_1');% Contour plotfigure;% Plot J_vals as 15 contours spaced logarithmically between 0.01 and 100contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))xlabel('\theta_0'); ylabel('\theta_1');hold on;plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);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 valuesm = 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.%之所以是X*theta是因为假设的h-theta(x)=theta0+theta1*x1J = sum((X*theta - y).^2) / (2 * m);% =========================================================================end
gradientDescent.m
function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)%GRADIENTDESCENT Performs gradient descent to learn theta% theta = GRADIENTDESENT(X, y, theta, alpha, num_iters) updates theta by % taking num_iters gradient steps with learning rate alpha% Initialize some useful valuesm = length(y); % number of training examplesJ_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;T = [0 ; 0];for i = 1 : m,T = T + (H(i) - y(i)) * X(i,:)';endtheta = theta - (alpha * T) / m; % ============================================================ % Save the cost J in every iteration J_history(iter) = computeCost(X, y, theta);endend
