%% 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
%%% Initialization
clear ; 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 =load('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.m
plotData(X, y);fprintf('Program paused. Press enter to continue.\n');
pause;%%=================== Part 3: Cost and Gradient descent ===================X =[ones(m,1),data(:,1)];% Add a column of ones to x
theta =zeros(2,1);% initialize fitting parameters % Some gradient descent settings
iterations =1500;
alpha =0.01;fprintf('\nTesting the cost function ...\n')% compute and display initial cost
J =computeCost(X, y, theta);fprintf('With theta = [0 ; 0]\nCost computed = %f\n', J);fprintf('Expected cost value (approx) 32.07\n');% further testing of the cost function
J =computeCost(X, y,[-1;2]);fprintf('\nWith theta = [-1 ; 2]\nCost computed = %f\n', J);fprintf('Expected cost value (approx) 54.24\n');fprintf('Program paused. Press enter to continue.\n');
pause;fprintf('\nRunning Gradient Descent ...\n')% run gradient descent
theta =gradientDescent(X, y, theta, alpha, iterations);% print theta to screen
fprintf('Theta found by gradient descent:\n');fprintf('%f\n', theta);fprintf('Expected theta values (approx)\n');fprintf(' -3.6303\n 1.1664\n\n');% Plot the linear fit
hold on;% keep previous plot visible
plot(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 35,000and70,000
predict1 =[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 J
theta0_vals =linspace(-10,10,100);
theta1_vals =linspace(-1,4,100);% initialize J_vals to a matrix of 0's
J_vals =zeros(length(theta0_vals),length(theta1_vals));% Fill out J_vals
for 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);end
end% Because of the way meshgrids work in the surf command, we need to
% transpose J_vals before calling surf,orelse the axes will be flipped
J_vals = J_vals';% Surface plot
figure;surf(theta0_vals, theta1_vals, J_vals)xlabel('\theta_0');ylabel('\theta_1');% Contour plot
figure;% Plot J_vals as 15 contours spaced logarithmically between 0.01and100contour(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);
各个函数具体实现如下：
plotData.m文件
function plotData(x, y)%PLOTDATA Plots the data points x and y into a new figure
%PLOTDATA(x,y) plots the data points and gives the figure axes labels of
% population and profit.figure;% open a new figure window%====================== YOUR CODE HERE ======================% Instructions: Plot the training data into a figure using the
%"figure"and"plot" commands. Set the axes labels using% the "xlabel"and"ylabel" commands. Assume the
% population and revenue data have been passed in
% as the x and y arguments of this function.%% Hint: You can use the 'rx' option with plot to have the markers
% appear as red crosses. Furthermore, you can make the
% markers larger by usingplot(...,'rx','MarkerSize',10);plot(x,y,'rx','MarkerSize',10);xlabel('Population of City in 10,100s'),ylabel('Profit in $10,000s');%============================================================
end
结果
computeCost.m文件
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;
error=(h-y).^2;
J=sum(error)/(2*m);%=========================================================================end
Testing the cost function … With theta = [0 ; 0] Cost computed = 32.072734 Expected cost value (approx) 32.07 With theta = [-1 ; 2] Cost computed = 54.242455 Expected cost value (approx) 54.24
gradientDescent.m文件
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.%theta=theta-alpha/m*X'*(X*theta-y);%============================================================% Save the cost J in every iteration J_history(iter)=computeCost(X, y, theta);endend
Running Gradient Descent … Theta found by gradient descent: -3.630291 1.166362 Expected theta values (approx) -3.6303 1.1664 For population = 35,000, we predict a profit of 4519.767868 For population = 70,000, we predict a profit of 45342.450129 Program paused. Press enter to continue.
