斯坦福机器学习公开课第一次编程作业

第一次编程作业跟着讲义感觉还是很简单，毕竟大部分代码都给了，自己只需要写一点点的算法实现，其实就是编写几个数学公式的事情，接上代码。
PS：博主在做一维的情况时对各个变量的计算进行了向量化，因此损失函数和梯度下降可以完全适应于多特征值的情况。
损失函数：

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.
s = 0;for iter=1:mh = theta' * X(iter,:)';s  = s + (h-y(iter))^2;
endJ = s/(2*m);% =========================================================================end

梯度下降：

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.%s = zeros(size(theta));for j = 1:mh = theta' * X(j,:)';s = s + (h-y(j)) * (X(j,:)');endtheta  = theta - alpha * s / m;% ============================================================% Save the cost J in every iteration    J_history(iter) = computeCost(X, y, theta);endend

Normal Equations：

function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression
%   NORMALEQN(X,y) computes the closed-form solution to linear
%   regression using the normal equations.theta = zeros(size(X, 2), 1);% ====================== YOUR CODE HERE ======================
% Instructions: Complete the code to compute the closed form solution
%               to linear regression and put the result in theta.
%% ---------------------- Sample Solution ----------------------
theta = inv(X'*X)*X'*y% -------------------------------------------------------------% ============================================================end

ex1_multi.m:

%% Machine Learning Online Class
%  Exercise 1: Linear regression with multiple variables
%
%  Instructions
%  ------------
%
%  This file contains code that helps you get started on the
%  linear regression 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 part of the exercise, you will need to change some
%  parts of the code below for various experiments (e.g., changing
%  learning rates).
%%% Initialization%% ================ Part 1: Feature Normalization ================%% Clear and Close Figures
clear ; close all; clcfprintf('Loading data ...\n');%% Load Data
data = load('ex1data2.txt');
X = data(:, 1:2);
y = data(:, 3);
m = length(y);% Print out some data points
fprintf('First 10 examples from the dataset: \n');
fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');fprintf('Program paused. Press enter to continue.\n');
pause;% Scale features and set them to zero mean
fprintf('Normalizing Features ...\n');[X mu sigma] = featureNormalize(X);% Add intercept term to X
X = [ones(m, 1) X];%% ================ Part 2: Gradient Descent ================% ====================== YOUR CODE HERE ======================
% Instructions: We have provided you with the following starter
%               code that runs gradient descent with a particular
%               learning rate (alpha).
%
%               Your task is to first make sure that your functions -
%               computeCost and gradientDescent already work with
%               this starter code and support multiple variables.
%
%               After that, try running gradient descent with
%               different values of alpha and see which one gives
%               you the best result.
%
%               Finally, you should complete the code at the end
%               to predict the price of a 1650 sq-ft, 3 br house.
%
% Hint: By using the 'hold on' command, you can plot multiple
%       graphs on the same figure.
%
% Hint: At prediction, make sure you do the same feature normalization.
%fprintf('Running gradient descent ...\n');% Choose some alpha value
alpha = 0.01;
num_iters = 400;% Init Theta and Run Gradient Descent
theta = zeros(3, 1);
[theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);% Plot the convergence graph
figure;
plot(1:numel(J_history), J_history, '-b', 'LineWidth', 2);
xlabel('Number of iterations');
ylabel('Cost J');% Display gradient descent's result
fprintf('Theta computed from gradient descent: \n');
fprintf(' %f \n', theta);
fprintf('\n');% Estimate the price of a 1650 sq-ft, 3 br house
% ====================== YOUR CODE HERE ======================
% Recall that the first column of X is all-ones. Thus, it does
% not need to be normalized.
price = theta' * [1;(1650-mu)/sigma;3]; % You should change this% ============================================================fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...'(using gradient descent):\n $%f\n'], price);fprintf('Program paused. Press enter to continue.\n');
pause;%% ================ Part 3: Normal Equations ================fprintf('Solving with normal equations...\n');% ====================== YOUR CODE HERE ======================
% Instructions: The following code computes the closed form
%               solution for linear regression using the normal
%               equations. You should complete the code in
%               normalEqn.m
%
%               After doing so, you should complete this code
%               to predict the price of a 1650 sq-ft, 3 br house.
%%% Load Data
data = csvread('ex1data2.txt');
X = data(:, 1:2);
y = data(:, 3);
m = length(y);% Add intercept term to X
X = [ones(m, 1) X];% Calculate the parameters from the normal equation
theta = normalEqn(X, y);% Display normal equation's result
fprintf('Theta computed from the normal equations: \n');
fprintf(' %f \n', theta);
fprintf('\n');% Estimate the price of a 1650 sq-ft, 3 br house
% ====================== YOUR CODE HERE ======================
price = theta' * [1;1650;3]; % You should change this% ============================================================fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...'(using normal equations):\n $%f\n'], price);

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