Coursera: Machine Learning-Andrew NG (Week 4) [Assignment Solution]

These solutions are for reference only.

try to solve on your own

but if you get stuck in between than you can refer these solutions

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lrCostFunction.m

function [J, grad] = lrCostFunction(theta, X, y, lambda)
%LRCOSTFUNCTION Compute cost and gradient for logistic regression with 
%regularization
%   J = LRCOSTFUNCTION(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));

h_theta = sigmoid(X * theta);

% Cost

J = (1/m) * (((-1 * y') * log(h_theta)) - ((1-y') * log(1-h_theta))) + (lambda/(2*m)) * (sum(theta(2:end) .^ 2));

temp = theta;
temp(1) = 0;

grad = ((1 / m) * X' * (h_theta - y)) + (lambda / m) * temp;
grad = grad(:);



end

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); % 10 * 401

% 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 
     
     % Variable 'X' contains data in dimension (5000 * 400). 
     % 5000 = Total no. of training examples, 400 = 400 pixels / training sample (digit image)
     % Total no. Features  = 400
     
    for c = 1:num_labels 
        all_theta(c,:) = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);
        % remember y (5000*1) is an array of labels i.e. it contains actual 
        % digit names (y==c) will return a vector with values 0 or 1. 1 at places where y==c 
        
        % 't' is passed as dummy parameter which is initialized with 'initial_theta' first
        % then subsequent values are choosen by fmincg [Note: Its not a builtin function like fminunc
        
        % fmincg will consider all training data having label c (1-10 note
        % 0 is mapped to 10) and find the optimal theta vector for it (Classifying white pixels with gray pixels). same
        % process is repeated for other classes
    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); % 10

% You need to return the following variables correctly 
p = zeros(size(X, 1), 1); % 5000 * 1

% Add ones to the X data matrix
X = [ones(m, 1) X]; % 5000 * 401

% ====================== 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.
%       
predict = sigmoid(X*all_theta'); % 5000 * 401 by 401*10
[~, p] = max(predict, [], 2);

% M = max(A,[],dim) returns the largest elements along dimension dim.
% For example, if A is a matrix, then max(A,[],2) is a column vector 
% containing the maximum value of each row.
end

predict.m

function p = predict(Theta1, Theta2, X)
%PREDICT Predict the label of an input given a trained neural network
%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
%   trained weights of a neural network (Theta1, Theta2)

% Useful values
m = size(X, 1);
num_labels = size(Theta2, 1);

% You need to return the following variables correctly 
p = zeros(size(X, 1), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the following code to make predictions using
%               your learned neural network. You should set p to a 
%               vector containing labels between 1 to num_labels.
%
% Hint: The max function might come in useful. 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.
%

X = [ones(m, 1) X];
t1 = sigmoid(X * Theta1');
t1 = [ones(m, 1) t1];

t2 = sigmoid( t1 * Theta2');

[~, p] = max(t2, [], 2);

end