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author Jordi Gutiérrez Hermoso <jordigh@octave.org>
date Sat, 29 Oct 2011 20:37:50 -0500
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1 %% Machine Learning Online Class - Exercise 2: Logistic Regression
2 %
3 % Instructions
4 % ------------
5 %
6 % This file contains code that helps you get started on the logistic
7 % regression exercise. You will need to complete the following functions
8 % in this exericse:
9 %
10 % sigmoid.m
11 % costFunction.m
12 % predict.m
13 % costFunctionReg.m
14 %
15 % For this exercise, you will not need to change any code in this file,
16 % or any other files other than those mentioned above.
17 %
18
19 %% Initialization
20 clear ; close all; clc
21
22 %% Load Data
23 % The first two columns contains the exam scores and the third column
24 % contains the label.
25
26 data = load('ex2data1.txt');
27 X = data(:, [1, 2]); y = data(:, 3);
28
29 %% ==================== Part 1: Plotting ====================
30 % We start the exercise by first plotting the data to understand the
31 % the problem we are working with.
32
33 fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
34 'indicating (y = 0) examples.\n']);
35
36 plotData(X, y);
37
38 % Put some labels
39 hold on;
40 % Labels and Legend
41 xlabel('Exam 1 score')
42 ylabel('Exam 2 score')
43
44 % Specified in plot order
45 legend('Admitted', 'Not admitted')
46 hold off;
47
48 fprintf('\nProgram paused. Press enter to continue.\n');
49 pause;
50
51
52 %% ============ Part 2: Compute Cost and Gradient ============
53 % In this part of the exercise, you will implement the cost and gradient
54 % for logistic regression. You neeed to complete the code in
55 % costFunction.m
56
57 % Setup the data matrix appropriately, and add ones for the intercept term
58 [m, n] = size(X);
59
60 % Add intercept term to x and X_test
61 X = [ones(m, 1) X];
62
63 % Initialize fitting parameters
64 initial_theta = zeros(n + 1, 1);
65
66 % Compute and display initial cost and gradient
67 [cost, grad] = costFunction(initial_theta, X, y);
68
69 fprintf('Cost at initial theta (zeros): %f\n', cost);
70 fprintf('Gradient at initial theta (zeros): \n');
71 fprintf(' %f \n', grad);
72
73 fprintf('\nProgram paused. Press enter to continue.\n');
74 pause;
75
76
77 %% ============= Part 3: Optimizing using fminunc =============
78 % In this exercise, you will use a built-in function (fminunc) to find the
79 % optimal parameters theta.
80
81 % Set options for fminunc
82 options = optimset('GradObj', 'on', 'MaxIter', 400);
83
84 % Run fminunc to obtain the optimal theta
85 % This function will return theta and the cost
86 [theta, cost] = ...
87 fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
88
89 % Print theta to screen
90 fprintf('Cost at theta found by fminunc: %f\n', cost);
91 fprintf('theta: \n');
92 fprintf(' %f \n', theta);
93
94 % Plot Boundary
95 plotDecisionBoundary(theta, X, y);
96
97 % Put some labels
98 hold on;
99 % Labels and Legend
100 xlabel('Exam 1 score')
101 ylabel('Exam 2 score')
102
103 % Specified in plot order
104 legend('Admitted', 'Not admitted')
105 hold off;
106
107 fprintf('\nProgram paused. Press enter to continue.\n');
108 pause;
109
110 %% ============== Part 4: Predict and Accuracies ==============
111 % After learning the parameters, you'll like to use it to predict the outcomes
112 % on unseen data. In this part, you will use the logistic regression model
113 % to predict the probability that a student with score 20 on exam 1 and
114 % score 80 on exam 2 will be admitted.
115 %
116 % Furthermore, you will compute the training and test set accuracies of
117 % our model.
118 %
119 % Your task is to complete the code in predict.m
120
121 % Predict probability for a student with score 45 on exam 1
122 % and score 85 on exam 2
123
124 prob = sigmoid([1 45 85] * theta);
125 fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
126 'probability of %f\n\n'], prob);
127
128 % Compute accuracy on our training set
129 p = predict(theta, X);
130
131 fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
132
133 fprintf('\nProgram paused. Press enter to continue.\n');
134 pause;
135