【DeepLearning】Exercise: Implement deep networks for digit classification

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.

z2 = stack{1}.w * data + repmat(stack{1}.b,1,size(data,2));
a2 = sigmoid(z2);
z3 = stack{2}.w * a2 + repmat(stack{2}.b,1,size(a2,2));
a3 = sigmoid(z3);

result = softmaxTheta * a3;
% sort by column
[~,ind] = sort(result);
pred = ind(size(softmaxTheta,1), :);

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

end


% You might find this useful
function sigm = sigmoid(x)
    sigm = 1 ./ (1 + exp(-x));
end

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
% inputSize: 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 is a hiddenSizeL1*numCases matrix
z2 = stack{1}.w * data + repmat(stack{1}.b,1,numCases);
% a2 is a hiddenSizeL1*numCases matrix
a2 = sigmoid(z2);
% z3 is a hiddenSizeL2*numCases matrix
z3 = stack{2}.w * a2 + repmat(stack{2}.b,1,numCases);
% a3 is a hiddenSizeL2*numCases matrix
a3 = sigmoid(z3);

weightDecay = (1/2) * lambda * sum(sum(softmaxTheta.*softmaxTheta));

M = softmaxTheta * a3;
M1 = bsxfun(@minus, M, max(M, [], 1));
M2 = bsxfun(@rdivide, exp(M1), sum(exp(M1)));
M = groundTruth .* log(M2);

cost = -(1/numCases) * sum(sum(M)) + weightDecay;

% difference between ground truth and predict value
diff = groundTruth - M2;
for i=1:numClasses
    softmaxThetaGrad(i,:) = -(1/numCases) * sum((a3 .* repmat(diff(i,:), hiddenSize, 1)) ,2)‘ + lambda * softmaxTheta(i,:);
end

% delta3 is a hiddenSizeL2*numCases matrix
delta3 = -(softmaxTheta‘ * (groundTruth-M2)) .* sigmoidDiff(z3);
% delta2 is a hiddenSizeL1*numCases vector
delta2 = ((stack{2}.w)‘ * delta3) .* sigmoidDiff(z2);

stackgrad{1}.w = delta2 * data‘ ./ numCases;
stackgrad{2}.w = delta3 * a2‘ ./ numCases;
stackgrad{1}.b = sum(delta2,2) ./ numCases;
stackgrad{2}.b = sum(delta3,2) ./ numCases;
% -------------------------------------------------------------------------

%% Roll gradient vector
grad = [softmaxThetaGrad(:) ; stack2params(stackgrad)];

end


% You might find this useful
function sigm = sigmoid(x)
    sigm = 1 ./ (1 + exp(-x));
end

% define the differential of sigmoid
function sigmDiff = sigmoidDiff(x)
sigmDiff = sigmoid(x) .* (1-sigmoid(x));
end

%% 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 0: 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‘);
trainData = trainData(:,1:30000);
trainLabels = loadMNISTLabels(‘mnist/train-labels-idx1-ubyte‘);
trainLabels = trainLabels(1:30000);
trainLabels(trainLabels == 0) = 10; % Remap 0 to 10 since our labels need to start from 1

%%======================================================================
%% STEP 1: 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);

% W1 = reshape(sae1OptTheta(1:hiddenSizeL1 * inputSize), hiddenSizeL1, inputSize);
% display_network(W1‘);
% -------------------------------------------------------------------------



%%======================================================================
%% 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(:);

%% ----------------- YOUR CODE HERE ----------------------
%  Use softmaxTrain.m from the previous exercise to train a multi-class
%  classifier. 

%  Use lambda = 1e-4 for the weight regularization for softmax

% You need to compute softmaxModel using softmaxTrain on trainFeatures and
% trainLabels
lambda = 1e-4;

options2.maxIter = 400;

softmaxModel = softmaxTrain(hiddenSizeL2, numClasses, lambda, ...
                            sae2Features, trainLabels, options2);

saeSoftmaxOptTheta = softmaxModel.optTheta(:);

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



%%======================================================================
%% STEP 4: 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".
%
%

opttheta = stackedAETheta; 

%  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‘;


[stackedAEOptTheta, cost] = minFunc( @(p) stackedAECost(p, ...
                                   inputSize, hiddenSizeL2, ...
                                   numClasses, netconfig, ...
                                   lambda, trainData, trainLabels), ...
                              stackedAETheta, options);


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



%%======================================================================
%% STEP 5: 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%%\n‘, acc * 100);

[pred] = stackedAEPredict(stackedAEOptTheta, inputSize, hiddenSizeL2, ...
                          numClasses, netconfig, testData);

acc = mean(testLabels(:) == pred(:));
fprintf(‘After Finetuning Test Accuracy: %0.3f%%\n‘, 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)