Skip to content
Permalink
Browse files

Programming Exercise 2

  • Loading branch information...
khanhnamle1994 committed Sep 6, 2017
1 parent 372374c commit 726ca4fc4ba72e4a1be04f5f38671ec6884a244e
Showing with 3,721 additions and 0 deletions.
  1. BIN machine-learning-ex2/ex2.pdf
  2. +35 −0 machine-learning-ex2/ex2/costFunction.m
  3. +40 −0 machine-learning-ex2/ex2/costFunctionReg.m
  4. +151 −0 machine-learning-ex2/ex2/ex2.m
  5. +136 −0 machine-learning-ex2/ex2/ex2_reg.m
  6. +100 −0 machine-learning-ex2/ex2/ex2data1.txt
  7. +118 −0 machine-learning-ex2/ex2/ex2data2.txt
  8. +41 −0 machine-learning-ex2/ex2/lib/jsonlab/AUTHORS.txt
  9. +74 −0 machine-learning-ex2/ex2/lib/jsonlab/ChangeLog.txt
  10. +25 −0 machine-learning-ex2/ex2/lib/jsonlab/LICENSE_BSD.txt
  11. +394 −0 machine-learning-ex2/ex2/lib/jsonlab/README.txt
  12. +32 −0 machine-learning-ex2/ex2/lib/jsonlab/jsonopt.m
  13. +566 −0 machine-learning-ex2/ex2/lib/jsonlab/loadjson.m
  14. +528 −0 machine-learning-ex2/ex2/lib/jsonlab/loadubjson.m
  15. +33 −0 machine-learning-ex2/ex2/lib/jsonlab/mergestruct.m
  16. +475 −0 machine-learning-ex2/ex2/lib/jsonlab/savejson.m
  17. +504 −0 machine-learning-ex2/ex2/lib/jsonlab/saveubjson.m
  18. +40 −0 machine-learning-ex2/ex2/lib/jsonlab/varargin2struct.m
  19. +30 −0 machine-learning-ex2/ex2/lib/makeValidFieldName.m
  20. +179 −0 machine-learning-ex2/ex2/lib/submitWithConfiguration.m
  21. +21 −0 machine-learning-ex2/ex2/mapFeature.m
  22. BIN machine-learning-ex2/ex2/octave-workspace
  23. +28 −0 machine-learning-ex2/ex2/plotData.m
  24. +48 −0 machine-learning-ex2/ex2/plotDecisionBoundary.m
  25. +28 −0 machine-learning-ex2/ex2/predict.m
  26. +18 −0 machine-learning-ex2/ex2/sigmoid.m
  27. +62 −0 machine-learning-ex2/ex2/submit.m
  28. +15 −0 machine-learning-ex2/ex2/token.mat
Binary file not shown.
@@ -0,0 +1,35 @@
function [J, grad] = costFunction(theta, X, y)
%COSTFUNCTION Compute cost and gradient for logistic regression
% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
% parameter for logistic regression and the gradient of the cost
% w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta
%
% Note: grad should have the same dimensions as theta
%

predictions = sigmoid(X*theta);

leftPart = -y' * log(predictions);

rightPart = (1 - y') * log(1 - predictions);

J = (1 / m) * (leftPart - rightPart);

grad = (1 / m) * ((predictions - y)' * X);

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

end
@@ -0,0 +1,40 @@
function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
% theta as the parameter for regularized logistic regression and the
% gradient of the cost w.r.t. to the parameters.

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
% You should set J to the cost.
% Compute the partial derivatives and set grad to the partial
% derivatives of the cost w.r.t. each parameter in theta

predictions = sigmoid(X*theta);

leftPart = -y' * log(predictions);

rightPart = (1 - y') * log(1 - predictions);

thetaZero = theta;

thetaZero(1) = 0;

lambaCostPart = (lambda / (2 * m)) * sum(thetaZero .^ 2);

lambdaGradPart = lambda / m * thetaZero;

J = (1 / m) * (leftPart - rightPart) + lambaCostPart;

grad = ((1/m) * (X' * (predictions - y))) + lambdaGradPart;

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

end
@@ -0,0 +1,151 @@
%% Machine Learning Online Class - Exercise 2: Logistic Regression
%
% Instructions
% ------------
%
% This file contains code that helps you get started on the logistic
% regression exercise. You will need to complete the following functions
% in this exericse:
%
% sigmoid.m
% costFunction.m
% predict.m
% costFunctionReg.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%

%% Initialization
clear ; close all; clc

%% Load Data
% The first two columns contains the exam scores and the third column
% contains the label.

data = load('ex2data1.txt');
X = data(:, [1, 2]); y = data(:, 3);

%% ==================== Part 1: Plotting ====================
% We start the exercise by first plotting the data to understand the
% the problem we are working with.

fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
'indicating (y = 0) examples.\n']);

plotData(X, y);

% Put some labels
hold on;
% Labels and Legend
xlabel('Exam 1 score')
ylabel('Exam 2 score')

% Specified in plot order
legend('Admitted', 'Not admitted')
hold off;

fprintf('\nProgram paused. Press enter to continue.\n');
pause;


%% ============ Part 2: Compute Cost and Gradient ============
% In this part of the exercise, you will implement the cost and gradient
% for logistic regression. You neeed to complete the code in
% costFunction.m

% Setup the data matrix appropriately, and add ones for the intercept term
[m, n] = size(X);

% Add intercept term to x and X_test
X = [ones(m, 1) X];

% Initialize fitting parameters
initial_theta = zeros(n + 1, 1);

% Compute and display initial cost and gradient
[cost, grad] = costFunction(initial_theta, X, y);

fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Expected cost (approx): 0.693\n');
fprintf('Gradient at initial theta (zeros): \n');
fprintf(' %f \n', grad);
fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');

% Compute and display cost and gradient with non-zero theta
test_theta = [-24; 0.2; 0.2];
[cost, grad] = costFunction(test_theta, X, y);

fprintf('\nCost at test theta: %f\n', cost);
fprintf('Expected cost (approx): 0.218\n');
fprintf('Gradient at test theta: \n');
fprintf(' %f \n', grad);
fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');

fprintf('\nProgram paused. Press enter to continue.\n');
pause;


%% ============= Part 3: Optimizing using fminunc =============
% In this exercise, you will use a built-in function (fminunc) to find the
% optimal parameters theta.

% Set options for fminunc
options = optimset('GradObj', 'on', 'MaxIter', 400);

% Run fminunc to obtain the optimal theta
% This function will return theta and the cost
[theta, cost] = ...
fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);

% Print theta to screen
fprintf('Cost at theta found by fminunc: %f\n', cost);
fprintf('Expected cost (approx): 0.203\n');
fprintf('theta: \n');
fprintf(' %f \n', theta);
fprintf('Expected theta (approx):\n');
fprintf(' -25.161\n 0.206\n 0.201\n');

% Plot Boundary
plotDecisionBoundary(theta, X, y);

% Put some labels
hold on;
% Labels and Legend
xlabel('Exam 1 score')
ylabel('Exam 2 score')

% Specified in plot order
legend('Admitted', 'Not admitted')
hold off;

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ============== Part 4: Predict and Accuracies ==============
% After learning the parameters, you'll like to use it to predict the outcomes
% on unseen data. In this part, you will use the logistic regression model
% to predict the probability that a student with score 45 on exam 1 and
% score 85 on exam 2 will be admitted.
%
% Furthermore, you will compute the training and test set accuracies of
% our model.
%
% Your task is to complete the code in predict.m

% Predict probability for a student with score 45 on exam 1
% and score 85 on exam 2

prob = sigmoid([1 45 85] * theta);
fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
'probability of %f\n'], prob);
fprintf('Expected value: 0.775 +/- 0.002\n\n');

% Compute accuracy on our training set
p = predict(theta, X);

fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('Expected accuracy (approx): 89.0\n');
fprintf('\n');


@@ -0,0 +1,136 @@
%% Machine Learning Online Class - Exercise 2: Logistic Regression
%
% Instructions
% ------------
%
% This file contains code that helps you get started on the second part
% of the exercise which covers regularization with logistic regression.
%
% You will need to complete the following functions in this exericse:
%
% sigmoid.m
% costFunction.m
% predict.m
% costFunctionReg.m
%
% For this exercise, you will not need to change any code in this file,
% or any other files other than those mentioned above.
%

%% Initialization
clear ; close all; clc

%% Load Data
% The first two columns contains the X values and the third column
% contains the label (y).

data = load('ex2data2.txt');
X = data(:, [1, 2]); y = data(:, 3);

plotData(X, y);

% Put some labels
hold on;

% Labels and Legend
xlabel('Microchip Test 1')
ylabel('Microchip Test 2')

% Specified in plot order
legend('y = 1', 'y = 0')
hold off;


%% =========== Part 1: Regularized Logistic Regression ============
% In this part, you are given a dataset with data points that are not
% linearly separable. However, you would still like to use logistic
% regression to classify the data points.
%
% To do so, you introduce more features to use -- in particular, you add
% polynomial features to our data matrix (similar to polynomial
% regression).
%

% Add Polynomial Features

% Note that mapFeature also adds a column of ones for us, so the intercept
% term is handled
X = mapFeature(X(:,1), X(:,2));

% Initialize fitting parameters
initial_theta = zeros(size(X, 2), 1);

% Set regularization parameter lambda to 1
lambda = 1;

% Compute and display initial cost and gradient for regularized logistic
% regression
[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);

fprintf('Cost at initial theta (zeros): %f\n', cost);
fprintf('Expected cost (approx): 0.693\n');
fprintf('Gradient at initial theta (zeros) - first five values only:\n');
fprintf(' %f \n', grad(1:5));
fprintf('Expected gradients (approx) - first five values only:\n');
fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

% Compute and display cost and gradient
% with all-ones theta and lambda = 10
test_theta = ones(size(X,2),1);
[cost, grad] = costFunctionReg(test_theta, X, y, 10);

fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
fprintf('Expected cost (approx): 3.16\n');
fprintf('Gradient at test theta - first five values only:\n');
fprintf(' %f \n', grad(1:5));
fprintf('Expected gradients (approx) - first five values only:\n');
fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');

fprintf('\nProgram paused. Press enter to continue.\n');
pause;

%% ============= Part 2: Regularization and Accuracies =============
% Optional Exercise:
% In this part, you will get to try different values of lambda and
% see how regularization affects the decision coundart
%
% Try the following values of lambda (0, 1, 10, 100).
%
% How does the decision boundary change when you vary lambda? How does
% the training set accuracy vary?
%

% Initialize fitting parameters
initial_theta = zeros(size(X, 2), 1);

% Set regularization parameter lambda to 1 (you should vary this)
lambda = 1;

% Set Options
options = optimset('GradObj', 'on', 'MaxIter', 400);

% Optimize
[theta, J, exit_flag] = ...
fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);

% Plot Boundary
plotDecisionBoundary(theta, X, y);
hold on;
title(sprintf('lambda = %g', lambda))

% Labels and Legend
xlabel('Microchip Test 1')
ylabel('Microchip Test 2')

legend('y = 1', 'y = 0', 'Decision boundary')
hold off;

% Compute accuracy on our training set
p = predict(theta, X);

fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');

0 comments on commit 726ca4f

Please sign in to comment.
You can’t perform that action at this time.