Coursera机器学习-Week 5-编程作业:Neural Network Learning

上周末本来是要搞定这个的，结果死活无法加载出来 Coursera C o u r s e r a 的视频，到周一才反应过来是不是 VPN V P N 的问题，然后一看果然是……最开始错怪 Coursera C o u r s e r a 了。

1.3 & 1.4 nnCostFunction.m

计算花费并且对其正则化。

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.
%

% 计算各层的结果
a1 = [ones(m, 1) X];
z2 = Theta1 * a1';
a2 = sigmoid(z2);
a2 = [ones(1, m); a2];
z3 = Theta2 * a2;
a3 = sigmoid(z3);

% 将 y 向量化
yVec = zeros(num_labels, m);
for i = 1 : m
  yVec(y(i), i) = 1;
end;

% 累加 m 组测试数据的花费
for i = 1 : m
  J += sum(-1 * yVec(:, i) .* log(a3(:, i)) - (1 - yVec(:, i)) .* log(1 - a3(:, i)));
end; 
J = J / m;

% 正则化处理（bias unit 不参与正则化）
J = J + lambda * (sum(sum(Theta1(:, 2 : end) .^ 2)) + sum(sum(Theta2(:, 2 : end) .^ 2))) / 2 / m;

% 反向传播吖
Delta1 = zeros(size(Theta1));
Delta2 = zeros(size(Theta2));

for i = 1 : m
  delta3 = a3(:, i) - yVec(:, i)
  delta2 = (Theta2' * delta3)(2 : end, :) .* sigmoidGradient(z2(:, i));
  Delta2 += delta3 * a2(:, i)';
  Delta1 += delta2 * a1(i, :);
end;

Theta2_grad = Delta2 / m;
Theta1_grad = Delta1 / m;

% 正则化梯度
Theta2_grad(:, 2 : end) = Theta2_grad(:, 2 : end) .+ lambda * Theta2(:, 2 : end) / m;
Theta1_grad(:, 2 : end) = Theta1_grad(:, 2 : end) .+ lambda * Theta1(:, 2 : end) / m;

% -------------------------------------------------------------

% =========================================================================

% Unroll gradients
grad = [Theta1_grad(:) ; Theta2_grad(:)];

end

2.1 sigmoidGradient.m

function g = sigmoidGradient(z)
%SIGMOIDGRADIENT returns the gradient of the sigmoid function
%evaluated at z
%   g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function
%   evaluated at z. This should work regardless if z is a matrix or a
%   vector. In particular, if z is a vector or matrix, you should return
%   the gradient for each element.

g = zeros(size(z));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the gradient of the sigmoid function evaluated at
%               each value of z (z can be a matrix, vector or scalar).

g = sigmoid(z) .* (1 - sigmoid(z));

% =============================================================

end

2.2 randInitializeWeights.m

在初始 θ θ 的时候，每次选择某一层的 θ θ ，然后让该层所有的 θ θ 都随机选取，范围 [−ϵinit，ϵinit] [ − ϵ i n i t ， ϵ i n i t ] 。

参考：

function W = randInitializeWeights(L_in, L_out)
%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
%incoming connections and L_out outgoing connections
%   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights 
%   of a layer with L_in incoming connections and L_out outgoing 
%   connections. 
%
%   Note that W should be set to a matrix of size(L_out, 1 + L_in) as
%   the first column of W handles the "bias" terms
%

% You need to return the following variables correctly 
W = zeros(L_out, 1 + L_in);

% ====================== YOUR CODE HERE ======================
% Instructions: Initialize W randomly so that we break the symmetry while
%               training the neural network.
%
% Note: The first column of W corresponds to the parameters for the bias unit
%

epsilon_init = 0.12
W = rand(L_out, 1 + L_in) * 2 * epsilon_init - epsilon_init;

% =========================================================================

end

结果

这周代码貌似挺少的，不过看英文文档依然是最大的障碍。