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nhs000 committed Jul 4, 2018
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17 changes: 17 additions & 0 deletions machine-learning-ex1/ex1/computeCost.m
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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

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
% You should set J to the cost.
J = (1/(2*m))*sum(power((X*theta - y), 2));
% =========================================================================

end
21 changes: 21 additions & 0 deletions machine-learning-ex1/ex1/computeCostMulti.m
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function J = computeCostMulti(X, y, theta)
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
% J = COMPUTECOSTMULTI(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.

J = (1/(2*m))*sum(power((X*theta - y), 2));


% =========================================================================

end
137 changes: 137 additions & 0 deletions machine-learning-ex1/ex1/ex1.m
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%% 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 35,000 and 70,000
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, or else 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 0.01 and 100
contour(theta0_vals, theta1_vals, J_vals, logspace(-2, 3, 20))
xlabel('\theta_0'); ylabel('\theta_1');
hold on;
pause;
plot(theta(1), theta(2), 'rx', 'MarkerSize', 10, 'LineWidth', 2);
pause;
162 changes: 162 additions & 0 deletions machine-learning-ex1/ex1/ex1_multi.m
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%% 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,:)]');

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.

data = [1650 3];
data = (data - mu);
data = data./sigma;
price = [1 data] *theta;


% ============================================================

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 = 0; % You should change this
price = [1 1650 3]*theta;

% ============================================================

fprintf(['Predicted price of a 1650 sq-ft, 3 br house ' ...
'(using normal equations):\n $%f\n'], price);

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