Exercise: Implement deep networks for digit classification
习题链接：Exercise: Implement deep networks for digit classification
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. numCases = size(data, 2); % forward z2 = stack{1}.w * data + repmat(stack{1}.b, 1, numCases); a2 = sigmoid(z2); z3 = stack{2}.w * a2 + repmat(stack{2}.b, 1, numCases); a3 = sigmoid(z3); [~, pred] = max(softmaxTheta * a3); % ----------------------------------------------------------- end % You might find this useful function sigm = sigmoid(x) sigm = 1 ./ (1 + exp(-x)); end
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 numCases = size(data, 2); groundTruth = full(sparse(labels, 1:numCases, 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. % z2 = stack{1}.w * data + repmat(stack{1}.b, 1, numCases); a2 = sigmoid(z2); z3 = stack{2}.w * a2 + repmat(stack{2}.b, 1, numCases); a3 = sigmoid(z3); M = softmaxTheta * a3; M = bsxfun(@minus, M, max(M, [], 1)); M = exp(M); M = bsxfun(@rdivide, M, sum(M)); diff = groundTruth - M; cost = -(1/numCases) * sum(sum(groundTruth .* log(M))) + (lambda/2) * sum(sum(softmaxTheta .* softmaxTheta)); for i=1:numClasses softmaxThetaGrad(i, :) = -(1/numCases) * (sum(a3 .* repmat(diff(i, :), hiddenSize, 1), 2))' + lambda * softmaxTheta(i, :); end delta3 = - (softmaxTheta' * diff) .* sigmoiddiff(z3); stackgrad{2}.w = delta3 * (a2)' ./ numCases; stackgrad{2}.b = sum(delta3, 2)./ numCases; delta2 = (stack{2}.w' * delta3) .* sigmoiddiff(z2); stackgrad{1}.w = delta2 * data'./ numCases; stackgrad{1}.b = sum(delta2, 2)./ numCases; % ------------------------------------------------------------------------- %% Roll gradient vector grad = [softmaxThetaGrad(:) ; stack2params(stackgrad)]; end % You might find this useful function sigm = sigmoid(x) sigm = 1 ./ (1 + exp(-x)); end function sigmdiff = sigmoiddiff(x) sigmdiff = sigmoid(x) .* (1 - sigmoid(x)); end
stackedAEExercise.m
%% CS294A/CS294W Stacked Autoencoder Exercise % Instructions % ------------ % % This file contains code that helps you get started on the % sstacked autoencoder exercise. You will need to complete code in % stackedAECost.m % You will also need to have implemented sparseAutoencoderCost.m and % softmaxCost.m from previous exercises. You will need the initializeParameters.m % loadMNISTImages.m, and loadMNISTLabels.m files from previous exercises. % % 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. 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 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 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'; [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.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, % softmaxCost.m satisfies this. minFuncOptions.display = 'on'; [saeSoftmaxOptTheta, cost] = minFunc( @(p) softmaxCost(p, ... numClasses, hiddenSizeL2, lambda, ... sae2Features, trainLabels), ... saeSoftmaxTheta, options); % ------------------------------------------------------------------------- %%====================================================================== %% 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 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". % % 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, % softmaxCost.m satisfies this. minFuncOptions.display = 'on'; [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)
Before Finetuning Test Accuracy: 87.740%
After Finetuning Test Accuracy: 97.610%