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"""
This tutorial introduces denoising auto-encoders (dA) 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 numpy
import theano
import theano.tensor as T
from theano.tensor.shared_randomstreams import RandomStreams
from logistic_sgd import load_data
from utils import tile_raster_images
import PIL.Image
class dA(object):
"""Denoising Auto-Encoder class (dA)
A denoising autoencoders tries to reconstruct the input from a corrupted
version of it by projecting it first in a latent space and reprojecting
it afterwards back in the input space. Please refer to Vincent et al.,2008
for more details. If x is the input then equation (1) computes a partially
destroyed version of x by means of a stochastic mapping q_D. Equation (2)
computes the projection of the input into the latent space. Equation (3)
computes the reconstruction of the input, while equation (4) computes the
reconstruction error.
.. math::
\tilde{x} ~ q_D(\tilde{x}|x) (1)
y = s(W \tilde{x} + b) (2)
x = s(W' y + b') (3)
L(x,z) = -sum_{k=1}^d [x_k \log z_k + (1-x_k) \log( 1-z_k)] (4)
"""
def __init__(self, numpy_rng, theano_rng=None, input=None,
n_visible=784, n_hidden=500,
W=None, bhid=None, bvis=None):
"""
Initialize the dA class by specifying the number of visible units (the
dimension d of the input ), the number of hidden units ( the dimension
d' of the latent or hidden space ) and the corruption level. The
constructor also receives symbolic variables for the input, weights and
bias. Such a symbolic variables are useful when, for example the input
is the result of some computations, or when weights are shared between
the dA and an MLP layer. When dealing with SdAs this always happens,
the dA on layer 2 gets as input the output of the dA on layer 1,
and the weights of the dA are used in the second stage of training
to construct an MLP.
:type numpy_rng: numpy.random.RandomState
:param numpy_rng: number random generator used to generate 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 input: theano.tensor.TensorType
:param input: a symbolic description of the input or None for
standalone dA
:type n_visible: int
:param n_visible: number of visible units
:type n_hidden: int
:param n_hidden: number of hidden units
:type W: theano.tensor.TensorType
:param W: Theano variable pointing to a set of weights that should be
shared belong the dA and another architecture; if dA should
be standalone set this to None
:type bhid: theano.tensor.TensorType
:param bhid: Theano variable pointing to a set of biases values (for
hidden units) that should be shared belong dA and another
architecture; if dA should be standalone set this to None
:type bvis: theano.tensor.TensorType
:param bvis: Theano variable pointing to a set of biases values (for
visible units) that should be shared belong dA and another
architecture; if dA should be standalone set this to None
"""
self.n_visible = n_visible
self.n_hidden = n_hidden
# create a Theano random generator that gives symbolic random values
if not theano_rng:
theano_rng = RandomStreams(numpy_rng.randint(2 ** 30))
# note : W' was written as `W_prime` and b' as `b_prime`
if not W:
# W is initialized with `initial_W` which is uniformely sampled
# from -4*sqrt(6./(n_visible+n_hidden)) and
# 4*sqrt(6./(n_hidden+n_visible))the output of uniform if
# converted using asarray to dtype
# theano.config.floatX so that the code is runable on GPU
initial_W = numpy.asarray(numpy_rng.uniform(
low=-4 * numpy.sqrt(6. / (n_hidden + n_visible)),
high=4 * numpy.sqrt(6. / (n_hidden + n_visible)),
size=(n_visible, n_hidden)), dtype=theano.config.floatX)
W = theano.shared(value=initial_W, name='W', borrow=True)
if not bvis:
bvis = theano.shared(value=numpy.zeros(n_visible,
dtype=theano.config.floatX),
borrow=True)
if not bhid:
bhid = theano.shared(value=numpy.zeros(n_hidden,
dtype=theano.config.floatX),
name='b',
borrow=True)
self.W = W
# b corresponds to the bias of the hidden
self.b = bhid
# b_prime corresponds to the bias of the visible
self.b_prime = bvis
# tied weights, therefore W_prime is W transpose
self.W_prime = self.W.T
self.theano_rng = theano_rng
# if no input is given, generate a variable representing the input
if input == None:
# we use a matrix because we expect a minibatch of several
# examples, each example being a row
self.x = T.dmatrix(name='input')
else:
self.x = input
self.params = [self.W, self.b, self.b_prime]
def get_corrupted_input(self, input, corruption_level):
"""This function keeps ``1-corruption_level`` entries of the inputs the
same and zero-out randomly selected subset of size ``coruption_level``
Note : first argument of theano.rng.binomial is the shape(size) of
random numbers that it should produce
second argument is the number of trials
third argument is the probability of success of any trial
this will produce an array of 0s and 1s where 1 has a
probability of 1 - ``corruption_level`` and 0 with
``corruption_level``
The binomial function return int64 data type by
default. int64 multiplicated by the input
type(floatX) always return float64. To keep all data
in floatX when floatX is float32, we set the dtype of
the binomial to floatX. As in our case the value of
the binomial is always 0 or 1, this don't change the
result. This is needed to allow the gpu to work
correctly as it only support float32 for now.
"""
return self.theano_rng.binomial(size=input.shape, n=1,
p=1 - corruption_level,
dtype=theano.config.floatX) * input
def get_hidden_values(self, input):
""" Computes the values of the hidden layer """
return T.nnet.sigmoid(T.dot(input, self.W) + self.b)
def get_reconstructed_input(self, hidden):
"""Computes the reconstructed input given the values of the
hidden layer
"""
return T.nnet.sigmoid(T.dot(hidden, self.W_prime) + self.b_prime)
def get_cost_updates(self, corruption_level, learning_rate):
""" This function computes the cost and the updates for one trainng
step of the dA """
tilde_x = self.get_corrupted_input(self.x, corruption_level)
y = self.get_hidden_values(tilde_x)
z = self.get_reconstructed_input(y)
# note : we sum over the size of a datapoint; if we are using
# minibatches, L will be a vector, with one entry per
# example in minibatch
L = - T.sum(self.x * T.log(z) + (1 - self.x) * T.log(1 - z), axis=1)
# note : L is now a vector, where each element is the
# cross-entropy cost of the reconstruction of the
# corresponding example of the minibatch. We need to
# compute the average of all these to get the cost of
# the minibatch
cost = T.mean(L)
# compute the gradients of the cost of the `dA` with respect
# to its parameters
gparams = T.grad(cost, self.params)
# generate the list of updates
updates = []
for param, gparam in zip(self.params, gparams):
updates.append((param, param - learning_rate * gparam))
return (cost, updates)
def test_dA(learning_rate=0.1, training_epochs=15,
dataset='../data/mnist.pkl.gz',
batch_size=20, output_folder='dA_plots'):
"""
This demo is tested on MNIST
:type learning_rate: float
:param learning_rate: learning rate used for training the DeNosing
AutoEncoder
:type training_epochs: int
:param training_epochs: number of epochs used for training
:type dataset: string
:param dataset: path to the picked dataset
"""
datasets = load_data(dataset)
train_set_x, train_set_y = datasets[0]
# compute number of minibatches for training, validation and testing
n_train_batches = train_set_x.get_value(borrow=True).shape[0] / batch_size
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
x = T.matrix('x') # the data is presented as rasterized images
if not os.path.isdir(output_folder):
os.makedirs(output_folder)
os.chdir(output_folder)
####################################
# BUILDING THE MODEL NO CORRUPTION #
####################################
rng = numpy.random.RandomState(123)
theano_rng = RandomStreams(rng.randint(2 ** 30))
da = dA(numpy_rng=rng, theano_rng=theano_rng, input=x,
n_visible=28 * 28, n_hidden=500)
cost, updates = da.get_cost_updates(corruption_level=0.,
learning_rate=learning_rate)
train_da = theano.function([index], cost, updates=updates,
givens={x: train_set_x[index * batch_size:
(index + 1) * batch_size]})
start_time = time.clock()
############
# TRAINING #
############
# go through training epochs
for epoch in xrange(training_epochs):
# go through trainng set
c = []
for batch_index in xrange(n_train_batches):
c.append(train_da(batch_index))
print 'Training epoch %d, cost ' % epoch, numpy.mean(c)
end_time = time.clock()
training_time = (end_time - start_time)
print >> sys.stderr, ('The no corruption code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((training_time) / 60.))
image = PIL.Image.fromarray(
tile_raster_images(X=da.W.get_value(borrow=True).T,
img_shape=(28, 28), tile_shape=(10, 10),
tile_spacing=(1, 1)))
image.save('filters_corruption_0.png')
#####################################
# BUILDING THE MODEL CORRUPTION 30% #
#####################################
rng = numpy.random.RandomState(123)
theano_rng = RandomStreams(rng.randint(2 ** 30))
da = dA(numpy_rng=rng, theano_rng=theano_rng, input=x,
n_visible=28 * 28, n_hidden=500)
cost, updates = da.get_cost_updates(corruption_level=0.3,
learning_rate=learning_rate)
train_da = theano.function([index], cost, updates=updates,
givens={x: train_set_x[index * batch_size:
(index + 1) * batch_size]})
start_time = time.clock()
############
# TRAINING #
############
# go through training epochs
for epoch in xrange(training_epochs):
# go through trainng set
c = []
for batch_index in xrange(n_train_batches):
c.append(train_da(batch_index))
print 'Training epoch %d, cost ' % epoch, numpy.mean(c)
end_time = time.clock()
training_time = (end_time - start_time)
print >> sys.stderr, ('The 30% corruption code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % (training_time / 60.))
image = PIL.Image.fromarray(tile_raster_images(
X=da.W.get_value(borrow=True).T,
img_shape=(28, 28), tile_shape=(10, 10),
tile_spacing=(1, 1)))
image.save('filters_corruption_30.png')
os.chdir('../')
if __name__ == '__main__':
test_dA()
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