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author | dumitru@dumitru.mtv.corp.google.com |
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date | Mon, 31 May 2010 19:07:59 -0700 |
parents | 4bc5eeec6394 |
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""" This tutorial introduces stacked denoising auto-encoders (SdA) using Theano. Denoising autoencoders are the building blocks for SdA. They are based on auto-encoders as the ones used in Bengio et al. 2007. An autoencoder takes an input x and first maps it to a hidden representation y = f_{\theta}(x) = s(Wx+b), parameterized by \theta={W,b}. The resulting latent representation y is then mapped back to a "reconstructed" vector z \in [0,1]^d in input space z = g_{\theta'}(y) = s(W'y + b'). The weight matrix W' can optionally be constrained such that W' = W^T, in which case the autoencoder is said to have tied weights. The network is trained such that to minimize the reconstruction error (the error between x and z). For the denosing autoencoder, during training, first x is corrupted into \tilde{x}, where \tilde{x} is a partially destroyed version of x by means of a stochastic mapping. Afterwards y is computed as before (using \tilde{x}), y = s(W\tilde{x} + b) and z as s(W'y + b'). The reconstruction error is now measured between z and the uncorrupted input x, which is computed as the cross-entropy : - \sum_{k=1}^d[ x_k \log z_k + (1-x_k) \log( 1-z_k)] References : - P. Vincent, H. Larochelle, Y. Bengio, P.A. Manzagol: Extracting and Composing Robust Features with Denoising Autoencoders, ICML'08, 1096-1103, 2008 - Y. Bengio, P. Lamblin, D. Popovici, H. Larochelle: Greedy Layer-Wise Training of Deep Networks, Advances in Neural Information Processing Systems 19, 2007 """ import numpy, time, cPickle, gzip import theano import theano.tensor as T from theano.tensor.shared_randomstreams import RandomStreams from logistic_sgd import LogisticRegression, load_data from mlp import HiddenLayer from dA import dA class SdA(object): """Stacked denoising auto-encoder class (SdA) A stacked denoising autoencoder model is obtained by stacking several dAs. The hidden layer of the dA at layer `i` becomes the input of the dA at layer `i+1`. The first layer dA gets as input the input of the SdA, and the hidden layer of the last dA represents the output. Note that after pretraining, the SdA is dealt with as a normal MLP, the dAs are only used to initialize the weights. """ def __init__(self, numpy_rng, theano_rng = None, n_ins = 784, hidden_layers_sizes = [500,500], n_outs = 10, corruption_levels = [0.1, 0.1]): """ This class is made to support a variable number of layers. :type numpy_rng: numpy.random.RandomState :param numpy_rng: numpy random number generator used to draw initial weights :type theano_rng: theano.tensor.shared_randomstreams.RandomStreams :param theano_rng: Theano random generator; if None is given one is generated based on a seed drawn from `rng` :type n_ins: int :param n_ins: dimension of the input to the sdA :type n_layers_sizes: list of ints :param n_layers_sizes: intermidiate layers size, must contain at least one value :type n_outs: int :param n_outs: dimension of the output of the network :type corruption_levels: list of float :param corruption_levels: amount of corruption to use for each layer """ self.sigmoid_layers = [] self.dA_layers = [] self.params = [] self.n_layers = len(hidden_layers_sizes) assert self.n_layers > 0 if not theano_rng: theano_rng = RandomStreams(numpy_rng.randint(2**30)) # allocate symbolic variables for the data self.x = T.matrix('x') # the data is presented as rasterized images self.y = T.ivector('y') # the labels are presented as 1D vector of # [int] labels # The SdA is an MLP, for which all weights of intermidiate layers # are shared with a different denoising autoencoders # We will first construct the SdA as a deep multilayer perceptron, # and when constructing each sigmoidal layer we also construct a # denoising autoencoder that shares weights with that layer # During pretraining we will train these autoencoders (which will # lead to chainging the weights of the MLP as well) # During finetunining we will finish training the SdA by doing # stochastich gradient descent on the MLP for i in xrange( self.n_layers ): # construct the sigmoidal layer # the size of the input is either the number of hidden units of # the layer below or the input size if we are on the first layer if i == 0 : input_size = n_ins else: input_size = hidden_layers_sizes[i-1] # the input to this layer is either the activation of the hidden # layer below or the input of the SdA if you are on the first # layer if i == 0 : layer_input = self.x else: layer_input = self.sigmoid_layers[-1].output sigmoid_layer = HiddenLayer(rng = numpy_rng, input = layer_input, n_in = input_size, n_out = hidden_layers_sizes[i], activation = T.nnet.sigmoid) # add the layer to our list of layers self.sigmoid_layers.append(sigmoid_layer) # its arguably a philosophical question... # but we are going to only declare that the parameters of the # sigmoid_layers are parameters of the StackedDAA # the visible biases in the dA are parameters of those # dA, but not the SdA self.params.extend(sigmoid_layer.params) # Construct a denoising autoencoder that shared weights with this # layer dA_layer = dA(numpy_rng = numpy_rng, theano_rng = theano_rng, input = layer_input, n_visible = input_size, n_hidden = hidden_layers_sizes[i], W = sigmoid_layer.W, bhid = sigmoid_layer.b) self.dA_layers.append(dA_layer) # We now need to add a logistic layer on top of the MLP self.logLayer = LogisticRegression(\ input = self.sigmoid_layers[-1].output,\ n_in = hidden_layers_sizes[-1], n_out = n_outs) self.params.extend(self.logLayer.params) # construct a function that implements one step of finetunining # compute the cost for second phase of training, # defined as the negative log likelihood self.finetune_cost = self.logLayer.negative_log_likelihood(self.y) # compute the gradients with respect to the model parameters # symbolic variable that points to the number of errors made on the # minibatch given by self.x and self.y self.errors = self.logLayer.errors(self.y) def pretraining_functions(self, train_set_x, batch_size): ''' Generates a list of functions, each of them implementing one step in trainnig the dA corresponding to the layer with same index. The function will require as input the minibatch index, and to train a dA you just need to iterate, calling the corresponding function on all minibatch indexes. :type train_set_x: theano.tensor.TensorType :param train_set_x: Shared variable that contains all datapoints used for training the dA :type batch_size: int :param batch_size: size of a [mini]batch :type learning_rate: float :param learning_rate: learning rate used during training for any of the dA layers ''' # index to a [mini]batch index = T.lscalar('index') # index to a minibatch corruption_level = T.scalar('corruption') # amount of corruption to use learning_rate = T.scalar('lr') # learning rate to use # number of batches n_batches = train_set_x.value.shape[0] / batch_size # begining of a batch, given `index` batch_begin = index * batch_size # ending of a batch given `index` batch_end = batch_begin+batch_size pretrain_fns = [] for dA in self.dA_layers: # get the cost and the updates list cost,updates = dA.get_cost_updates( corruption_level, learning_rate) # compile the theano function fn = theano.function( inputs = [index, theano.Param(corruption_level, default = 0.2), theano.Param(learning_rate, default = 0.1)], outputs = cost, updates = updates, givens = {self.x :train_set_x[batch_begin:batch_end]}) # append `fn` to the list of functions pretrain_fns.append(fn) return pretrain_fns def build_finetune_functions(self, datasets, batch_size, learning_rate): '''Generates a function `train` that implements one step of finetuning, a function `validate` that computes the error on a batch from the validation set, and a function `test` that computes the error on a batch from the testing set :type datasets: list of pairs of theano.tensor.TensorType :param datasets: It is a list that contain all the datasets; the has to contain three pairs, `train`, `valid`, `test` in this order, where each pair is formed of two Theano variables, one for the datapoints, the other for the labels :type batch_size: int :param batch_size: size of a minibatch :type learning_rate: float :param learning_rate: learning rate used during finetune stage ''' (train_set_x, train_set_y) = datasets[0] (valid_set_x, valid_set_y) = datasets[1] (test_set_x , test_set_y ) = datasets[2] # compute number of minibatches for training, validation and testing n_valid_batches = valid_set_x.value.shape[0] / batch_size n_test_batches = test_set_x.value.shape[0] / batch_size index = T.lscalar('index') # index to a [mini]batch # compute the gradients with respect to the model parameters gparams = T.grad(self.finetune_cost, self.params) # compute list of fine-tuning updates updates = {} for param, gparam in zip(self.params, gparams): updates[param] = param - gparam*learning_rate train_fn = theano.function(inputs = [index], outputs = self.finetune_cost, updates = updates, givens = { self.x : train_set_x[index*batch_size:(index+1)*batch_size], self.y : train_set_y[index*batch_size:(index+1)*batch_size]}) test_score_i = theano.function([index], self.errors, givens = { self.x: test_set_x[index*batch_size:(index+1)*batch_size], self.y: test_set_y[index*batch_size:(index+1)*batch_size]}) valid_score_i = theano.function([index], self.errors, givens = { self.x: valid_set_x[index*batch_size:(index+1)*batch_size], self.y: valid_set_y[index*batch_size:(index+1)*batch_size]}) # Create a function that scans the entire validation set def valid_score(): return [valid_score_i(i) for i in xrange(n_valid_batches)] # Create a function that scans the entire test set def test_score(): return [test_score_i(i) for i in xrange(n_test_batches)] return train_fn, valid_score, test_score def test_SdA( finetune_lr = 0.1, pretraining_epochs = 15, \ pretrain_lr = 0.1, training_epochs = 1000, \ dataset='mnist.pkl.gz'): """ Demonstrates how to train and test a stochastic denoising autoencoder. This is demonstrated on MNIST. :type learning_rate: float :param learning_rate: learning rate used in the finetune stage (factor for the stochastic gradient) :type pretraining_epochs: int :param pretraining_epochs: number of epoch to do pretraining :type pretrain_lr: float :param pretrain_lr: learning rate to be used during pre-training :type n_iter: int :param n_iter: maximal number of iterations ot run the optimizer :type dataset: string :param dataset: path the the pickled dataset """ datasets = load_data(dataset) train_set_x, train_set_y = datasets[0] valid_set_x, valid_set_y = datasets[1] test_set_x , test_set_y = datasets[2] batch_size = 20 # size of the minibatch # compute number of minibatches for training, validation and testing n_train_batches = train_set_x.value.shape[0] / batch_size # numpy random generator numpy_rng = numpy.random.RandomState(123) print '... building the model' # construct the stacked denoising autoencoder class sda = SdA( numpy_rng = numpy_rng, n_ins = 28*28, hidden_layers_sizes = [1000,1000,1000], n_outs = 10) ######################### # PRETRAINING THE MODEL # ######################### print '... getting the pretraining functions' pretraining_fns = sda.pretraining_functions( train_set_x = train_set_x, batch_size = batch_size ) print '... pre-training the model' start_time = time.clock() ## Pre-train layer-wise for i in xrange(sda.n_layers): # go through pretraining epochs for epoch in xrange(pretraining_epochs): # go through the training set c = [] for batch_index in xrange(n_train_batches): c.append( pretraining_fns[i](index = batch_index, corruption = 0.2, lr = pretrain_lr ) ) print 'Pre-training layer %i, epoch %d, cost '%(i,epoch),numpy.mean(c) end_time = time.clock() print ('Pretraining took %f minutes' %((end_time-start_time)/60.)) ######################## # FINETUNING THE MODEL # ######################## # get the training, validation and testing function for the model print '... getting the finetuning functions' train_fn, validate_model, test_model = sda.build_finetune_functions ( datasets = datasets, batch_size = batch_size, learning_rate = finetune_lr) print '... finetunning the model' # early-stopping parameters patience = 10000 # look as this many examples regardless patience_increase = 2. # wait this much longer when a new best is # found improvement_threshold = 0.995 # a relative improvement of this much is # considered significant validation_frequency = min(n_train_batches, patience/2) # go through this many # minibatche before checking the network # on the validation set; in this case we # check every epoch best_params = None best_validation_loss = float('inf') test_score = 0. start_time = time.clock() done_looping = False epoch = 0 while (epoch < training_epochs) and (not done_looping): epoch = epoch + 1 for minibatch_index in xrange(n_train_batches): minibatch_avg_cost = train_fn(minibatch_index) iter = epoch * n_train_batches + minibatch_index if (iter+1) % validation_frequency == 0: validation_losses = validate_model() this_validation_loss = numpy.mean(validation_losses) print('epoch %i, minibatch %i/%i, validation error %f %%' % \ (epoch, minibatch_index+1, n_train_batches, \ this_validation_loss*100.)) # if we got the best validation score until now if this_validation_loss < best_validation_loss: #improve patience if loss improvement is good enough if this_validation_loss < best_validation_loss * \ improvement_threshold : patience = max(patience, iter * patience_increase) # save best validation score and iteration number best_validation_loss = this_validation_loss best_iter = iter # test it on the test set test_losses = test_model() test_score = numpy.mean(test_losses) print((' epoch %i, minibatch %i/%i, test error of best ' 'model %f %%') % (epoch, minibatch_index+1, n_train_batches, test_score*100.)) if patience <= iter : done_looping = True break end_time = time.clock() print(('Optimization complete with best validation score of %f %%,' 'with test performance %f %%') % (best_validation_loss * 100., test_score*100.)) print ('The code ran for %f minutes' % ((end_time-start_time)/60.)) if __name__ == '__main__': test_SdA()