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‎machine-learning-ex2/ex2.pdf

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‎machine-learning-ex2/ex2/costFunction.m

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function [J, grad] = costFunction(theta, X, y)
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%COSTFUNCTION Compute cost and gradient for logistic regression
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% J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
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% parameter for logistic regression and the gradient of the cost
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% w.r.t. to the parameters.
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% Initialize some useful values
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m = length(y); % number of training examples
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% You need to return the following variables correctly
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J = 0;
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grad = zeros(size(theta));
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the cost of a particular choice of theta.
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% You should set J to the cost.
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% Compute the partial derivatives and set grad to the partial
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% derivatives of the cost w.r.t. each parameter in theta
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%
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% Note: grad should have the same dimensions as theta
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%
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J= -1 * sum( y .* log( sigmoid(X*theta) ) + (1 - y ) .* log( (1 - sigmoid(X*theta)) ) ) / m ;
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grad = ( X' * (sigmoid(X*theta) - y ) )/ m ;
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% =============================================================
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end

‎machine-learning-ex2/ex2/costFunctionReg.m

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function [J, grad] = costFunctionReg(theta, X, y, lambda)
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%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
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% J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
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% theta as the parameter for regularized logistic regression and the
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% gradient of the cost w.r.t. to the parameters.
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% Initialize some useful values
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m = length(y); % number of training examples
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% You need to return the following variables correctly
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J = 0;
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grad = zeros(size(theta));
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% ====================== YOUR CODE HERE ======================
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% Instructions: Compute the cost of a particular choice of theta.
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% You should set J to the cost.
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% Compute the partial derivatives and set grad to the partial
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% derivatives of the cost w.r.t. each parameter in theta
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theta_1=[0;theta(2:end)]; % 先把theta(1)拿掉，不参与正则化
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J= -1 * sum( y .* log( sigmoid(X*theta) ) + (1 - y ) .* log( (1 - sigmoid(X*theta)) ) ) / m + lambda/(2*m) * theta_1' * theta_1 ;
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grad = ( X' * (sigmoid(X*theta) - y ) )/ m + lambda/m * theta_1 ;
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% =============================================================
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end

‎machine-learning-ex2/ex2/ex2.m

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%% Machine Learning Online Class - Exercise 2: Logistic Regression
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the logistic
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% regression exercise. You will need to complete the following functions
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% in this exericse:
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%
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% sigmoid.m
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% costFunction.m
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% predict.m
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% costFunctionReg.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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%% Initialization
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clear ; close all; clc
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%% Load Data
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% The first two columns contains the exam scores and the third column
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% contains the label.
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data = load('ex2data1.txt');
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X = data(:, [1, 2]); y = data(:, 3);
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%% ==================== Part 1: Plotting ====================
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% We start the exercise by first plotting the data to understand the
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% the problem we are working with.
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fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
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'indicating (y = 0) examples.\n']);
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plotData(X, y);
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% Put some labels
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hold on;
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% Labels and Legend
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xlabel('Exam 1 score')
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ylabel('Exam 2 score')
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% Specified in plot order
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legend('Admitted', 'Not admitted')
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hold off;
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============ Part 2: Compute Cost and Gradient ============
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% In this part of the exercise, you will implement the cost and gradient
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% for logistic regression. You neeed to complete the code in
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% costFunction.m
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% Setup the data matrix appropriately, and add ones for the intercept term
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[m, n] = size(X);
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% Add intercept term to x and X_test
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X = [ones(m, 1) X];
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% Initialize fitting parameters
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initial_theta = zeros(n + 1, 1);
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% Compute and display initial cost and gradient
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[cost, grad] = costFunction(initial_theta, X, y);
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fprintf('Cost at initial theta (zeros): %f\n', cost);
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fprintf('Expected cost (approx): 0.693\n');
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fprintf('Gradient at initial theta (zeros): \n');
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fprintf(' %f \n', grad);
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fprintf('Expected gradients (approx):\n -0.1000\n -12.0092\n -11.2628\n');
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% Compute and display cost and gradient with non-zero theta
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test_theta = [-24; 0.2; 0.2];
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[cost, grad] = costFunction(test_theta, X, y);
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fprintf('\nCost at test theta: %f\n', cost);
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fprintf('Expected cost (approx): 0.218\n');
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fprintf('Gradient at test theta: \n');
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fprintf(' %f \n', grad);
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fprintf('Expected gradients (approx):\n 0.043\n 2.566\n 2.647\n');
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============= Part 3: Optimizing using fminunc =============
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% In this exercise, you will use a built-in function (fminunc) to find the
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% optimal parameters theta.
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% Set options for fminunc
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options = optimset('GradObj', 'on', 'MaxIter', 400);
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% Run fminunc to obtain the optimal theta
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% This function will return theta and the cost
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[theta, cost] = ...
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fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
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% Print theta to screen
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fprintf('Cost at theta found by fminunc: %f\n', cost);
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fprintf('Expected cost (approx): 0.203\n');
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fprintf('theta: \n');
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fprintf(' %f \n', theta);
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fprintf('Expected theta (approx):\n');
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fprintf(' -25.161\n 0.206\n 0.201\n');
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% Plot Boundary
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plotDecisionBoundary(theta, X, y);
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% Put some labels
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hold on;
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% Labels and Legend
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xlabel('Exam 1 score')
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ylabel('Exam 2 score')
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% Specified in plot order
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legend('Admitted', 'Not admitted')
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hold off;
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============== Part 4: Predict and Accuracies ==============
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% After learning the parameters, you'll like to use it to predict the outcomes
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% on unseen data. In this part, you will use the logistic regression model
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% to predict the probability that a student with score 45 on exam 1 and
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% score 85 on exam 2 will be admitted.
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%
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% Furthermore, you will compute the training and test set accuracies of
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% our model.
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%
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% Your task is to complete the code in predict.m
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% Predict probability for a student with score 45 on exam 1
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% and score 85 on exam 2
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prob = sigmoid([1 45 85] * theta);
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fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
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'probability of %f\n'], prob);
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fprintf('Expected value: 0.775 +/- 0.002\n\n');
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% Compute accuracy on our training set
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p = predict(theta, X);
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fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
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fprintf('Expected accuracy (approx): 89.0\n');
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fprintf('\n');
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‎machine-learning-ex2/ex2/ex2_reg.m

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%% Machine Learning Online Class - Exercise 2: Logistic Regression
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the second part
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% of the exercise which covers regularization with logistic regression.
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%
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% You will need to complete the following functions in this exericse:
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%
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% sigmoid.m
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% costFunction.m
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% predict.m
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% costFunctionReg.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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%% Initialization
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clear ; close all; clc
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%% Load Data
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% The first two columns contains the X values and the third column
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% contains the label (y).
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data = load('ex2data2.txt');
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X = data(:, [1, 2]); y = data(:, 3);
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plotData(X, y);
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% Put some labels
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hold on;
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% Labels and Legend
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xlabel('Microchip Test 1')
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ylabel('Microchip Test 2')
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% Specified in plot order
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legend('y = 1', 'y = 0')
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hold off;
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%% =========== Part 1: Regularized Logistic Regression ============
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% In this part, you are given a dataset with data points that are not
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% linearly separable. However, you would still like to use logistic
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% regression to classify the data points.
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%
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% To do so, you introduce more features to use -- in particular, you add
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% polynomial features to our data matrix (similar to polynomial
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% regression).
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%
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% Add Polynomial Features
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% Note that mapFeature also adds a column of ones for us, so the intercept
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% term is handled
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X = mapFeature(X(:,1), X(:,2));
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% Initialize fitting parameters
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initial_theta = zeros(size(X, 2), 1);
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% Set regularization parameter lambda to 1
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lambda = 1;
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% Compute and display initial cost and gradient for regularized logistic
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% regression
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[cost, grad] = costFunctionReg(initial_theta, X, y, lambda);
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fprintf('Cost at initial theta (zeros): %f\n', cost);
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fprintf('Expected cost (approx): 0.693\n');
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fprintf('Gradient at initial theta (zeros) - first five values only:\n');
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fprintf(' %f \n', grad(1:5));
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fprintf('Expected gradients (approx) - first five values only:\n');
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fprintf(' 0.0085\n 0.0188\n 0.0001\n 0.0503\n 0.0115\n');
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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% Compute and display cost and gradient
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% with all-ones theta and lambda = 10
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test_theta = ones(size(X,2),1);
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[cost, grad] = costFunctionReg(test_theta, X, y, 10);
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fprintf('\nCost at test theta (with lambda = 10): %f\n', cost);
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fprintf('Expected cost (approx): 3.16\n');
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fprintf('Gradient at test theta - first five values only:\n');
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fprintf(' %f \n', grad(1:5));
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fprintf('Expected gradients (approx) - first five values only:\n');
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fprintf(' 0.3460\n 0.1614\n 0.1948\n 0.2269\n 0.0922\n');
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% ============= Part 2: Regularization and Accuracies =============
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% Optional Exercise:
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% In this part, you will get to try different values of lambda and
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% see how regularization affects the decision coundart
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%
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% Try the following values of lambda (0, 1, 10, 100).
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%
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% How does the decision boundary change when you vary lambda? How does
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% the training set accuracy vary?
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%
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% Initialize fitting parameters
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initial_theta = zeros(size(X, 2), 1);
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% Set regularization parameter lambda to 1 (you should vary this)
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lambda = 1;
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% Set Options
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options = optimset('GradObj', 'on', 'MaxIter', 400);
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% Optimize
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[theta, J, exit_flag] = ...
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fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);
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% Plot Boundary
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plotDecisionBoundary(theta, X, y);
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hold on;
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title(sprintf('lambda = %g', lambda))
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% Labels and Legend
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xlabel('Microchip Test 1')
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ylabel('Microchip Test 2')
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legend('y = 1', 'y = 0', 'Decision boundary')
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hold off;
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% Compute accuracy on our training set
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p = predict(theta, X);
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fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
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fprintf('Expected accuracy (with lambda = 1): 83.1 (approx)\n');
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