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Matlab gradient descent - Coursera's Machine Learning ex4/nnCostFunction.m
function [J grad] = nnCostFunction(nn_params, ...
input_layer_size, ...
hidden_layer_size, ...
num_labels, ...
X, Y, lambda)
%NNCOSTFUNCTION Implements the neural network cost function for a two layer
%neural network which performs classification
% [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
% X, y, lambda) computes the cost and gradient of the neural network. The
% parameters for the neural network are "unrolled" into the vector
% nn_params and need to be converted back into the weight matrices.
%
% The returned parameter grad should be a "unrolled" vector of the
% partial derivatives of the neural network.
%
% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
% for our 2 layer neural network
Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
hidden_layer_size, (input_layer_size + 1));
Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
num_labels, (hidden_layer_size + 1));
% Setup some useful variables
m = size(X, 1);
% You need to return the following variables correctly
% J = 0;
% Theta1_grad = zeros(size(Theta1));
% Theta2_grad = zeros(size(Theta2));
% ====================== YOUR CODE HERE ======================
% Instructions: You should complete the code by working through the
% following parts.
%
% Part 1: Feedforward the neural network and return the cost in the
% variable J. After implementing Part 1, you can verify that your
% cost function computation is correct by verifying the cost
% computed in ex4.m
% Allow arbitrary network architectures. Create cell array of all Theta parameters
Theta={Theta1; Theta2};
% Transform y from integers in 1:10 into vectors which would be returned by the
% output layer
YOutput = zeros(length(Y), rows(Theta{end}));
K = rows(Theta{end}); % Number of classes
for i = 1:length(Y)
% Expect integers from 1:
if (!(class = Y(i)) == floor(class) || class < 1 || class > K)
printf("unexpected value y(%d) = %f. Bailing.\n", i, class);
return
end
YOutput(i, Y(i)) = 1;
% Or, faster (but no validation):
% yv=[1:num_labels] == y % Use Broadcasting
% Or
% yv = bsxfun(@eq, y, 1:num_labels);
end
Y = YOutput;
%
% Compute unregularised cost (J)
%
% Get h(X) and z (non-activated output of all neurons in network)
[~, z, activation] = predict(Theta1, Theta2, X);
hX = activation{end};
J = 1/m * sum(sum((-Y .* log(hX) - (1 - Y) .* log(1 - hX))));
% Add regularisation
for i = 1:length(Theta)
J += lambda / 2 / m * sum(sum(Theta{i}(:,2:end) .^ 2));
end
%
% Compute gradients via backpropagation
%
% Get error of output layer
layers = 1 + length(Theta);
d{layers} = hX - Y;
% Propagate errors backwards through hidden layers
for layer = layers-1 : -1 : 2
d{layer} = d{layer+1} * Theta{layer};
d{layer} = d{layer}(:, 2:end); % Remove "error" for constant bias term
d{layer} .*= sigmoidGradient(z{layer});
end
% Calculate Theta gradients
for l = 1:layers-1
Theta_grad{l} = zeros(size(Theta{l}));
% Sum of outer products
Theta_grad{l} += d{l+1}' * [ones(m,1) activation{l}];
% Add regularisation term
Theta_grad{l}(:, 2:end) += lambda * Theta{l}(:, 2:end);
Theta_grad{l} /= m;
end
% Unroll gradients
grad=[];
for i = 1:length(Theta_grad)
grad = [grad; Theta_grad{i}(:)];
end
% ------- End of Ravi's code --------
% Part 2: Implement the backpropagation algorithm to compute the gradients
% Theta1_grad and Theta2_grad. You should return the partial derivatives of
% the cost function with respect to Theta1 and Theta2 in Theta1_grad and
% Theta2_grad, respectively. After implementing Part 2, you can check
% that your implementation is correct by running checkNNGradients
%
% Note: The vector y passed into the function is a vector of labels
% containing values from 1..K. You need to map this vector into a
% binary vector of 1's and 0's to be used with the neural network
% cost function.
%
% Hint: We recommend implementing backpropagation using a for-loop
% over the training examples if you are implementing it for the
% first time.
%
% Part 3: Implement regularization with the cost function and gradients.
%
% Hint: You can implement this around the code for
% backpropagation. That is, you can compute the gradients for
% the regularization separately and then add them to Theta1_grad
% and Theta2_grad from Part 2.
%
% -------------------------------------------------------------
% =========================================================================
end
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