前面记到了深度网络这一章。当时觉得练习应该挺简单的，用不了多少时间，结果训练时间真够长的...途中debug的时候还手贱的clear了一下，又得从头开始运行。不过最终还是调试成功了，sigh~
前一篇博文讲了深度网络的一些基本知识，这次讲义中的练习还是针对MNIST手写库，主要步骤是训练两个自编码器，然后进行softmax回归，最后再整体进行一次微调。
训练自编码器以及softmax回归都是利用前面已经写好的代码。微调部分的代码其实就是一次反向传播。
以下就是代码：
主程序部分：
stackedAEExercise.m
% For the purpose of completing the assignment, you do not need to % change the code in this file. % %%====================================================================== %% STEP 0: Here we provide the relevant parameters values that will % allow your sparse autoencoder to get good filters; you do not need to % change the parameters below. DISPLAY = true; inputSize = 28 * 28; numClasses = 10; hiddenSizeL1 = 200; % Layer 1 Hidden Size hiddenSizeL2 = 200; % Layer 2 Hidden Size sparsityParam = 0.1; % desired average activation of the hidden units. % (This was denoted by the Greek alphabet rho, which looks like a lower-case "p", % in the lecture notes). lambda = 3e-3; % weight decay parameter beta = 3; % weight of sparsity penalty term %%====================================================================== %% STEP 1: Load data from the MNIST database % % This loads our training data from the MNIST database files. % Load MNIST database files trainData = loadMNISTImages('mnist/train-images-idx3-ubyte'); trainLabels = loadMNISTLabels('mnist/train-labels-idx1-ubyte'); trainLabels(trainLabels == 0) = 10; % Remap 0 to 10 since our labels need to start from 1 %%====================================================================== %% STEP 2: Train the first sparse autoencoder % This trains the first sparse autoencoder on the unlabelled STL training % images. % If you've correctly implemented sparseAutoencoderCost.m, you don't need % to change anything here. % Randomly initialize the parameters sae1Theta = initializeParameters(hiddenSizeL1, inputSize); %% ---------------------- YOUR CODE HERE --------------------------------- % Instructions: Train the first layer sparse autoencoder, this layer has % an hidden size of "hiddenSizeL1" % You should store the optimal parameters in sae1OptTheta % Use minFunc to minimize the function addpath minFunc/ options.Method = 'lbfgs'; % Here, we use L-BFGS to optimize our cost % function. Generally, for minFunc to work, you % need a function pointer with two outputs: the % function value and the gradient. In our problem, % sparseAutoencoderCost.m satisfies this. options.maxIter = 400; % Maximum number of iterations of L-BFGS to run options.display = 'on'; [sae1optTheta, cost] = minFunc( @(p) sparseAutoencoderCost(p, ... inputSize, hiddenSizeL1, ... lambda, sparsityParam, ... beta, trainData), ... sae1Theta, options); %------------------------------------------------------------------------- %====================================================================== % STEP 2: Train the second sparse autoencoder %This trains the second sparse autoencoder on the first autoencoder %featurse. %If you've correctly implemented sparseAutoencoderCost.m, you don't need %to change anything here. [sae1Features] = feedForwardAutoencoder(sae1optTheta, hiddenSizeL1, ... inputSize, trainData); % Randomly initialize the parameters sae2Theta = initializeParameters(hiddenSizeL2, hiddenSizeL1); %% ---------------------- YOUR CODE HERE --------------------------------- % Instructions: Train the second layer sparse autoencoder, this layer has % an hidden size of "hiddenSizeL2" and an inputsize of % "hiddenSizeL1" % % You should store the optimal parameters in sae2OptTheta [sae2opttheta, cost] = minFunc( @(p) sparseAutoencoderCost(p, ... hiddenSizeL1, hiddenSizeL2, ... lambda, sparsityParam, ... beta, sae1Features), ... sae2Theta, options); %------------------------------------------------------------------------- %====================================================================== %% STEP 3: Train the softmax classifier % This trains the sparse autoencoder on the second autoencoder features. % If you've correctly implemented softmaxCost.m, you don't need % to change anything here. [sae2Features] = feedForwardAutoencoder(sae2opttheta, hiddenSizeL2, ... hiddenSizeL1, sae1Features); % Randomly initialize the parameters saeSoftmaxTheta = 0.005 * randn(hiddenSizeL2 * numClasses, 1); %% ---------------------- YOUR CODE HERE --------------------------------- % Instructions: Train the softmax classifier, the classifier takes in % input of dimension "hiddenSizeL2" corresponding to the % hidden layer size of the 2nd layer. % % You should store the optimal parameters in saeSoftmaxOptTheta % % NOTE: If you used softmaxTrain to complete this part of the exercise, % set saeSoftmaxOptTheta = softmaxModel.optTheta(:); options.maxIter = 100; softmax_lambda = 1e-4; numLabels = 10; softmaxModel = softmaxTrain(hiddenSizeL2, numLabels, softmax_lambda, ... sae2Features, trainLabels, options); saeSoftmaxOptTheta = softmaxModel.optTheta(:); %------------------------------------------------------------------------- %====================================================================== %% STEP 5: Finetune softmax model % Implement the stackedAECost to give the combined cost of the whole model % then run this cell. % Initialize the stack using the parameters learned inputSize = 28*28; stack = cell(2,1); stack{1}.w = reshape(sae1optTheta(1:hiddenSizeL1*inputSize), ... hiddenSizeL1, inputSize); stack{1}.b = sae1optTheta(2*hiddenSizeL1*inputSize+1:2*hiddenSizeL1*inputSize+hiddenSizeL1); stack{2}.w = reshape(sae2opttheta(1:hiddenSizeL2*hiddenSizeL1), ... hiddenSizeL2, hiddenSizeL1); stack{2}.b = sae2opttheta(2*hiddenSizeL2*hiddenSizeL1+1:2*hiddenSizeL2*hiddenSizeL1+hiddenSizeL2); % Initialize the parameters for the deep model [stackparams, netconfig] = stack2params(stack); stackedAETheta = [ saeSoftmaxOptTheta ; stackparams ]; %% ---------------------- YOUR CODE HERE --------------------------------- % Instructions: Train the deep network, hidden size here refers to the ' % dimension of the input to the classifier, which corresponds % to "hiddenSizeL2". % % [stackedAEOptTheta, cost] = minFunc( @(p) stackedAECost(p, inputSize, hiddenSizeL2, ... numClasses, netconfig, ... lambda, trainData, trainLabels), ... stackedAETheta,options); % ------------------------------------------------------------------------- %%====================================================================== %% STEP 6: Test % Instructions: You will need to complete the code in stackedAEPredict.m % before running this part of the code % % Get labelled test images % Note that we apply the same kind of preprocessing as the training set testData = loadMNISTImages('mnist/t10k-images-idx3-ubyte'); testLabels = loadMNISTLabels('mnist/t10k-labels-idx1-ubyte'); testLabels(testLabels == 0) = 10; % Remap 0 to 10 [pred] = stackedAEPredict(stackedAETheta, inputSize, hiddenSizeL2, ... numClasses, netconfig, testData); acc = mean(testLabels(:) == pred(:)); fprintf('Before Finetuning Test Accuracy: %0.3f%% ', acc * 100); [pred] = stackedAEPredict(stackedAEOptTheta, inputSize, hiddenSizeL2, ... numClasses, netconfig, testData); acc = mean(testLabels(:) == pred(:)); fprintf('After Finetuning Test Accuracy: %0.3f%% ', acc * 100); % Accuracy is the proportion of correctly classified images % The results for our implementation were: % % Before Finetuning Test Accuracy: 87.7% % After Finetuning Test Accuracy: 97.6% % % If your values are too low (accuracy less than 95%), you should check % your code for errors, and make sure you are training on the % entire data set of 60000 28x28 training images % (unless you modified the loading code, this should be the case)
微调部分的代价函数：
stackedAECost.m
function [ cost, grad ] = stackedAECost(theta, inputSize, hiddenSize, ... numClasses, netconfig, ... lambda, data, labels) % stackedAECost: Takes a trained softmaxTheta and a training data set with labels, % and returns cost and gradient using a stacked autoencoder model. Used for % finetuning. % theta: trained weights from the autoencoder % visibleSize: the number of input units % hiddenSize: the number of hidden units *at the 2nd layer* % numClasses: the number of categories % netconfig: the network configuration of the stack % lambda: the weight regularization penalty % data: Our matrix containing the training data as columns. So, data(:,i) is the i-th training example. % labels: A vector containing labels, where labels(i) is the label for the % i-th training example %% Unroll softmaxTheta parameter % We first extract the part which compute the softmax gradient softmaxTheta = reshape(theta(1:hiddenSize*numClasses), numClasses, hiddenSize); % Extract out the "stack" stack = params2stack(theta(hiddenSize*numClasses+1:end), netconfig); % You will need to compute the following gradients softmaxThetaGrad = zeros(size(softmaxTheta)); stackgrad = cell(size(stack)); for d = 1:numel(stack) stackgrad{d}.w = zeros(size(stack{d}.w)); stackgrad{d}.b = zeros(size(stack{d}.b)); end cost = 0; % You need to compute this % You might find these variables useful M = size(data, 2); groundTruth = full(sparse(labels, 1:M, 1)); %% --------------------------- YOUR CODE HERE ----------------------------- % Instructions: Compute the cost function and gradient vector for % the stacked autoencoder. % % You are given a stack variable which is a cell-array of % the weights and biases for every layer. In particular, you % can refer to the weights of Layer d, using stack{d}.w and % the biases using stack{d}.b . To get the total number of % layers, you can use numel(stack). % % The last layer of the network is connected to the softmax % classification layer, softmaxTheta. % % You should compute the gradients for the softmaxTheta, % storing that in softmaxThetaGrad. Similarly, you should % compute the gradients for each layer in the stack, storing % the gradients in stackgrad{d}.w and stackgrad{d}.b % Note that the size of the matrices in stackgrad should % match exactly that of the size of the matrices in stack. % %----------先计算a和z---------------- d = numel(stack); %stack的深度 n = d+1; %网络层数 a = cell(n,1); z = cell(n,1); a{1} = data; %a{1}设成输入数据 for l = 2:n %给a{2,...n}和z{2,,...n}赋值 z{l} = stack{l-1}.w * a{l-1} + repmat(stack{l-1}.b,[1,size(a{l-1},2)]); a{l} = sigmoid(z{l}); end %------------------------------------ %-------------计算softmax的代价函数和梯度函数------------- Ma = softmaxTheta * a{n}; NorM = bsxfun(@minus, Ma, max(Ma, [], 1)); %归一化，每列减去此列的最大值，使得M的每个元素不至于太大。 ExpM = exp(NorM); P = bsxfun(@rdivide,ExpM,sum(ExpM)); %概率 cost = -1/M*(groundTruth(:)'*log(P(:)))+lambda/2*(softmaxTheta(:)'*softmaxTheta(:)); %代价函数 softmaxThetaGrad = -1/M*((groundTruth-P)*a{n}') + lambda*softmaxTheta; %梯度 %-------------------------------------------------------- %--------------计算每一层的delta--------------------- delta = cell(n); delta{n} = -softmaxTheta'*(groundTruth-P).*(a{n}).*(1-a{n}); %可以参照前面讲义BP算法的实现 for l = n-1:-1:1 delta{l} = stack{l}.w' * delta{l+1}.*(a{l}).*(1-a{l}); end %---------------------------------------------------- %--------------计算每一层的w和b的梯度----------------- for l = n-1:-1:1 stackgrad{l}.w = (1/M)*delta{l+1}*a{l}'; stackgrad{l}.b = (1/M)*sum(delta{l+1},2); end %---------------------------------------------------- % ------------------------------------------------------------------------- %% Roll gradient vector grad = [softmaxThetaGrad(:) ; stack2params(stackgrad)]; end % You might find this useful function sigm = sigmoid(x) sigm = 1 ./ (1 + exp(-x)); end
预测函数：
stackedAEPredict.m
function [pred] = stackedAEPredict(theta, inputSize, hiddenSize, numClasses, netconfig, data) % stackedAEPredict: Takes a trained theta and a test data set, % and returns the predicted labels for each example. % theta: trained weights from the autoencoder % visibleSize: the number of input units % hiddenSize: the number of hidden units *at the 2nd layer* % numClasses: the number of categories % data: Our matrix containing the training data as columns. So, data(:,i) is the i-th training example. % Your code should produce the prediction matrix % pred, where pred(i) is argmax_c P(y(c) | x(i)). %% Unroll theta parameter % We first extract the part which compute the softmax gradient softmaxTheta = reshape(theta(1:hiddenSize*numClasses), numClasses, hiddenSize); % Extract out the "stack" stack = params2stack(theta(hiddenSize*numClasses+1:end), netconfig); %% ---------- YOUR CODE HERE -------------------------------------- % Instructions: Compute pred using theta assuming that the labels start % from 1. % %----------先计算a和z---------------- d = numel(stack); %stack的深度 n = d+1; %网络层数 a = cell(n,1); z = cell(n,1); a{1} = data; %a{1}设成输入数据 for l = 2:n %给a{2,...n}和z{2,,...n}赋值 z{l} = stack{l-1}.w * a{l-1} + repmat(stack{l-1}.b,[1,size(a{l-1},2)]); a{l} = sigmoid(z{l}); end %------------------------------------- M = softmaxTheta * a{n}; [Y,pred] = max(M,[],1); % ----------------------------------------------------------- end % You might find this useful function sigm = sigmoid(x) sigm = 1 ./ (1 + exp(-x)); end
最后结果：
跟讲义以及程序注释中有点差别，特别是没有微调的结果，讲义中提到是不到百分之九十的，这里算出来是百分之九十四左右：
但是微调后的结果基本是一样的。
PS:讲义地址：http://deeplearning.stanford.edu/wiki/index.php/Exercise:_Implement_deep_networks_for_digit_classification