Deep Learning by Andrew Ng --- stacked autoencoder
When should we use fine-tuning?
It is typically used only if you have a large labeled training set; in this setting, fine-tuning can significantly improve the performance of your classifier. However, if you have a large unlabeled dataset (for unsupervised feature learning/pre-training) and only a relatively small labeled training set, then fine-tuning is significantly less likely to help.
Stacked Autoencoders(Training):
相当于用多个autoencoder去捕获输入集的特征。第一个autoencoder捕获了数据集的特征后，得到特征matrix1（hidden layer的权重）.然后将特征matrix1与输入集feedForward处理后的activation作为输入去捕获更高等级的特征matrix2（hidden layer的权重）.然后不断重复，再讲最后得到的特征activation作为输入集输入到softmax classifier（或者其他分类器）中训练。（注意并非将训练完后得到的特征matrix直接传给下一个autoencoder，而是将输入集与此输入集同级的特征matrix用feedForward方法得到的activation传入下一个autoencoder,即将输出传给下一个autoencode）。
然后整个网络训练完之后，将各个步骤得到的特征matrix与分类器的参数合成新的网络。
fine-tuning:
其实就是将前面分步训练得到的hidden layer的Weight和softmax refression的softmaxTheta作为合成的神经网络的初始参数，然后运用神经网络的前馈和反向算法对初始参数进行微调（注意合成的网络是必须加上分类器的，不然也无法对神经网络的参数进行反向传播和微调（finetuning），此以softmax regression 为例）。具体可参考softmaxCost.m，sparseAutoencoderCost.m。
练习题答案（推荐自己先试着完成后参考）:
-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 = 40; % 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
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 = 40; % 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.maxIter = 100;
softmaxModel = softmaxTrain(hiddenSizeL2, 10, 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
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%%\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)
- 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 delta = 1:numel(stack)
stackgrad{delta}.w = zeros(size(stack{delta}.w));
stackgrad{delta}.b = zeros(size(stack{delta}.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));%input labels
%% --------------------------- 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.
%
% -------------------------------------------------------------------------
depth = numel(stack)% 神经网络的层数(不包括softmax层)
z = cell(depth+1,1);
a = cell(depth+1,1);%进行前馈神经网络计算所需要的参数
a{1} =data;%输入层
for index = 1:depth%前馈神经网络计算(为什么要加1)
z{index+1} = stack{index}.w*a{index}+repmat(stack{index}.b, 1, size(a{index},2));
a{index+1} = sigmoid(z{index+1});
end
model = softmaxTheta*a{depth+1}; %神经网络最后一层的activation传入softmax regression。
model = bsxfun(@minus, model , max(model , [], 1));
h = exp(model );
h = bsxfun(@rdivide, h, sum(h));
size(groundTruth);
cost = -1/numClasses*sum(sum(groundTruth.*log(h)))+lambda/2*sum(sum(softmaxTheta.^2));
softmaxThetaGrad = -1/numClasses*((groundTruth-h)*a{depth+1}')+lambda*softmaxTheta;
%反向传播算法
delta = cell(depth+1);
%I is the input labels and P is the vector of conditional probabilities.
delta{depth+1} = -(softmaxTheta' * (groundTruth - h)) .* a{depth+1} .* (1-a{depth+1});
for layer = (depth:-1:2)
delta{layer} = (stack{layer}.w' * delta{layer+1}) .* a{layer} .* (1-a{layer});
end
for layer = (depth:-1:1)
stackgrad{layer}.w = (1/numClasses) * delta{layer+1} * a{layer}';
stackgrad{layer}.b = (1/numClasses) * sum(delta{layer+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
- 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.
%前馈神经网络算法
depth = numel(stack);
z = cell(depth+1,1);
a = cell(depth+1, 1);
a{1} = data;
for layer = (1:depth)
z{layer+1} = stack{layer}.w * a{layer} + repmat(stack{layer}.b, [1, size(a{layer},2)]);
a{layer+1} = sigmoid(z{layer+1});
end
[index, pred] = max(softmaxTheta * a{depth+1});%预测
% -----------------------------------------------------------
end
% You might find this useful
function sigm = sigmoid(x)
sigm = 1 ./ (1 + exp(-x));
end