Cost function, gradient of regularized logistic regression for multi-class classification are similar to exercise 2.
This exercise implement one-vs-all classification by training multiple regularized logistic regression classifiers, one for each of the K classes in our dataset.
oneVsAll.m
function [all_theta] = oneVsAll(X, y, num_labels, lambda)
%ONEVSALL trains multiple logistic regression classifiers and returns all
%the classifiers in a matrix all_theta, where the i-th row of all_theta
%corresponds to the classifier for label i
% [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
% logisitc regression classifiers and returns each of these classifiers
% in a matrix all_theta, where the i-th row of all_theta corresponds
% to the classifier for label i
% Some useful variables
m = size(X, 1);
n = size(X, 2);
% You need to return the following variables correctly
all_theta = zeros(num_labels, n + 1);
% Add ones to the X data matrix
X = [ones(m, 1) X];
% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the following code to train num_labels
% logistic regression classifiers with regularization
% parameter lambda.
%
% Hint: theta(:) will return a column vector.
%
% Hint: You can use y == c to obtain a vector of 1's and 0's that tell use
% whether the ground truth is true/false for this class.
%
% Note: For this assignment, we recommend using fmincg to optimize the cost
% function. It is okay to use a for-loop (for c = 1:num_labels) to
% loop over the different classes.
%
% fmincg works similarly to fminunc, but is more efficient when we
% are dealing with large number of parameters.
%
% Example Code for fmincg:
%
% % Set Initial theta
% initial_theta = zeros(n + 1, 1);
%
% % Set options for fminunc
% options = optimset('GradObj', 'on', 'MaxIter', 50);
%
% % Run fmincg to obtain the optimal theta
% % This function will return theta and the cost
% [theta] = ...
% fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...
% initial_theta, options);
%
for i = 1:num_labels
initial_theta = zeros(n+1, 1);
options = optimset('GradObj', 'on', 'MaxIter', 50);
[theta] = fmincg(@(t)(lrCostFunction(t, X, (y == i), lambda)), ...
initial_theta, options);
all_theta(i,:) = theta';
end
% =========================================================================
end
predictOneVsAll.m
function p = predictOneVsAll(all_theta, X)
%PREDICT Predict the label for a trained one-vs-all classifier. The labels
%are in the range 1..K, where K = size(all_theta, 1).
% p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
% for each example in the matrix X. Note that X contains the examples in
% rows. all_theta is a matrix where the i-th row is a trained logistic
% regression theta vector for the i-th class. You should set p to a vector
% of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
% for 4 examples)
m = size(X, 1);
num_labels = size(all_theta, 1);
% You need to return the following variables correctly
p = zeros(size(X, 1), 1);
% Add ones to the X data matrix
X = [ones(m, 1) X];
% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
% your learned logistic regression parameters (one-vs-all).
% You should set p to a vector of predictions (from 1 to
% num_labels).
%
% Hint: This code can be done all vectorized using the max function.
% In particular, the max function can also return the index of the
% max element, for more information see 'help max'. If your examples
% are in rows, then, you can use max(A, [], 2) to obtain the max
% for each row.
%
all_ps = sigmoid(X*all_theta');
[p_max,i_max] = max(all_ps, [], 2);
p = i_max;
% =========================================================================
end