"""
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 cPickle
import gzip
import os
import sys
import time
import cPickle
import numpy
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: intermediate 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 intermediate 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') # % of corruption to use
learning_rate = T.scalar('lr') # learning rate to use
# number of batches
n_batches = train_set_x.get_value(borrow=True).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.get_value(borrow=True).shape[0]
n_valid_batches /= batch_size
n_test_batches = test_set_x.get_value(borrow=True).shape[0]
n_test_batches /= 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.append((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]},
name='train')
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]},
name='test')
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]},
name='valid')
# 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 save_params(self, filename):
output = open(filename, 'wb')
for p in range(len(self.params)):
cPickle.dump(self.params[p].get_value(), output)
output.close()
def load_params(self, filename):
pkl_file = open(filename, 'rb')
param_num = len(self.params)
for p in range(param_num):
self.params[p].set_value(cPickle.load(pkl_file))
pkl_file.close()
def test_SdA(finetune_lr=0.1, pretraining_epochs=15,
pretrain_lr=0.001, training_epochs=1000,
dataset='../data/mnist.pkl.gz', batch_size=1):
"""
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]
# compute number of minibatches for training, validation and testing
n_train_batches = train_set_x.get_value(borrow=True).shape[0]
n_train_batches /= batch_size
# numpy random generator
numpy_rng = numpy.random.RandomState(89677)
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
corruption_levels = [.1, .2, .3]
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=corruption_levels[i],
lr=pretrain_lr))
print 'Pre-training layer %i, epoch %d, cost ' % (i, epoch),
print numpy.mean(c)
end_time = time.clock()
print >> sys.stderr, ('The pretraining code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((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 = 10 * n_train_batches # 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 = numpy.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 - 1) * 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 >> sys.stderr, ('The training code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.))
if __name__ == '__main__':
test_SdA()
