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; clc
fprintf('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,:)]');
% Scale features and set them to zero mean
fprintf('Normalizing Features ...\n');
% 特征缩放
[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 = 4000;
% 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');
% 上图说明，随着迭代次数增加，损失函数逐步减小
% Display gradient descent's result
fprintf('Theta computed from gradient descent: \n');
fprintf(' %f \n', theta);
% 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 = [1, 1650, 3] * theta;
% % You should change this
% price = theta(1) + (1650 - mu(1)) / sigma(1) * theta(2) + (3 - mu(2)) / sigma(2) * theta(3);
price = [1, ((1650 - mu(1)) / sigma(1)), ((3 - mu(2)) / sigma(2))] * theta;
% ============================================================
fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
'(using gradient descent):\n $%f\n'], price);
================ 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);
% Estimate the price of a 1650 sq-ft, 3 br house
% ====================== YOUR CODE HERE ======================
price = [1, 1650, 3] * theta; % You should change this
% ============================================================
fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
'(using normal equations):\n $%f\n'], price);