AI/ML/DL相关|【题解】编程作业ex4: Neural Network Learning (Machine Learning) AI

吐槽：最近事情有点多，居然鸽到了下一周orz。。咳咳终于写完了= =顺便反向传播原理目前还不是非常理解，所以笔记也要鸽一阵orz。。。
题目：
Download the programming assignment here. This ZIP file contains the instructions in a PDF and the starter code. You may use either MATLAB or Octave (>= 3.8.0).

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nnCostFunction我的解法：
感觉其实从头到尾都在编写这个函数，所以我就只放了个这。。编写过程中需要验证输出size的我都注释了。。郁闷的地方在于求J的时候A都是可以用矩阵解决的，但是在求Y的时候用了1到m的循环，实在没想到什么不用循环的方法QAQ。。然后求grad的部分也不够简洁，算法都是直接按照pdf上面的步骤实现的。。
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
%
% 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.
%
% Add ones to the X data matrix
X = [ones(m, 1) X];
A1 = X;
Z2 = A1 * Theta1';
A2 = [ones(m, 1) sigmoid(Z2)];
Z3 = A2 * Theta2';
A3 = sigmoid(Z3);
H = A3;
all_y = [1: num_labels];
Y = zeros(m, num_labels);
for i = 1:m,
Y(i, :) = (all_y == y(i));
endfor
J = 1/m * sum(sum(-Y.*log(H)-(ones(size(Y))-Y).*log(1-H))) + lambda/(2*m)*(sum(sum(Theta1(:, 2:end).^2))+sum(sum(Theta2(:, 2:end).^2)))
%fprintf('A1 = %d*%d, A2 = %d*%d, A3 = %d*%d, Y = %d*%d\n', ...
%size(A1)(1),size(A1)(2),size(A2)(1),size(A2)(2),size(A3)(1),size(A3)(2),size(Y)(1),size(Y)(2));
% -------------------------------------------------------------
Delta_1 = zeros(size(Theta1));
Delta_2 = zeros(size(Theta2));
for t = 1:m,
% Step1
a_1 = A1(t, :)';
z_2 = Z2(t, :)';
a_2 = A2(t, :)';
z_3 = Z3(t, :)';
a_3 = A3(t, :)';
y_temp = Y(t, :)';
%fprintf('a_1 = %d*%d, a_2 = %d*%d, a_3 = %d*%d, y_temp = %d*%d\n', ...
%size(a_1)(1),size(a_1)(2),size(a_2)(1),size(a_2)(2),size(a_3)(1),size(a_3)(2),size(y_temp)(1),size(y_temp)(2));
% Step2
delta_3 = a_3 - y_temp;
% Step3
delta_2 = Theta2' * delta_3 .* sigmoidGradient([1; z_2]);
% Step4
delta_2 = delta_2(2:end);
%fprintf('delta_2 = %d*%d, a_1 = %d*%d\n',size(delta_2)(1),size(delta_2)(2),size(a_1)(1),size(a_1)(2));
Delta_1 = Delta_1 + delta_2 * a_1';
Delta_2 = Delta_2 + delta_3 * a_2';

endfor
% Step5
Theta1_grad = 1/m*Delta_1;
Theta2_grad = 1/m*Delta_2;
% regularization
Delta_para1 = lambda/m*ones(size(Theta1));
Delta_para1(:, 1) = 0;
Delta_para2 = lambda/m*ones(size(Theta2));
Delta_para2(:, 1) = 0;
Theta1_grad = Theta1_grad + Delta_para1 .* Theta1;
Theta2_grad = Theta2_grad + Delta_para2 .* Theta2;
% =========================================================================
% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];
【AI/ML/DL相关|【题解】编程作业ex4: Neural Network Learning (Machine Learning)】
end

AI/ML/DL相关|【题解】编程作业ex4: Neural Network Learning (Machine Learning)

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