Implement back propagation

ex4/nnCostFunction.m

@@ -72,6 +72,48 @@ assert(size(J) == [1 1]);
 %               over the training examples if you are implementing it for the
 %               first time.
 %
+
+D_1 = zeros(size(Theta1));
+D_2 = zeros(size(Theta2));
+
+for t = 1:m
+  % feed forward this training sample
+  % ---------------------------------------------------------------------------
+  a_1 = X(t,:);
+  % (X already has 1-column)
+  assert(size(a_1) == [1, input_layer_size+1]);
+
+  z_2 = a_1*Theta1';
+  a_2 = sigmoid(z_2);
+  a_2 = [ones(size(a_2, 1)), a_2];  % (bias term)
+  assert(size(a_2) == [1, hidden_layer_size+1]);
+
+  z_3 = a_2*Theta2';
+  a_3 = sigmoid(z_3);
+  h_0 = a_3;
+  assert(size(h_0) == [1, num_labels]);
+
+  % back propagate / error
+  % ---------------------------------------------------------------------------
+  assert(size(y) == [m num_labels]);
+  d_3 = a_3 - y(t,:);
+  assert(size(d_3) == [1, num_labels]);
+
+  d_2 = d_3*Theta2 .* [1, sigmoidGradient(z_2)];
+  d_2 = d_2(2:end);
+  assert(size(d_2) == [1, hidden_layer_size]);
+
+  % accumulate over all m training examples
+  D_2 = D_2 + d_3'*a_2;
+  D_1 = D_1 + d_2'*a_1;
+end
+
+% average
+D_2 /= m;
+D_1 /= m;
+Theta2_grad = D_2;
+Theta1_grad = D_1;
+
 % Part 3: Implement regularization with the cost function and gradients.
 %
 %         Hint: You can implement this around the code for