def __init__(self, numpy_rng, theano_rng=None, n_ins=784,
hidden_layers_sizes=[500, 500], n_outs=10):
"""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 DBN
:type hidden_layers_sizes: list of ints
:param hidden_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
"""
self.sigmoid_layers = []
self.rbm_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
# end-snippet-1
# The DBN is an MLP, for which all weights of intermediate
# layers are shared with a different RBM. We will first
# construct the DBN as a deep multilayer perceptron, and when
# constructing each sigmoidal layer we also construct an RBM
# that shares weights with that layer. During pretraining we
# will train these RBMs (which will lead to chainging the
# weights of the MLP as well) During finetuning we will finish
# training the DBN by doing stochastic 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 DBN 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 DBN. The visible
# biases in the RBM are parameters of those RBMs, but not
# of the DBN.
self.params.extend(sigmoid_layer.params)
# Construct an RBM that shared weights with this layer
rbm_layer = RBM(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,
hbias=sigmoid_layer.b)
self.rbm_layers.append(rbm_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)
# compute the cost for second phase of training, defined as the
# negative log likelihood of the logistic regression (output) layer
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)
class DBN(object):
"""Deep Belief Network
A deep belief network is obtained by stacking several RBMs on top of each
other. The hidden layer of the RBM at layer `i` becomes the input of the
RBM at layer `i+1`. The first layer RBM gets as input the input of the
network, and the hidden layer of the last RBM represents the output. When
used for classification, the DBN is treated as a MLP, by adding a logistic
regression layer on top.
"""
def __init__(self, numpy_rng, theano_rng=None, n_ins=784,
hidden_layers_sizes=[500, 500], n_outs=10):
"""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 DBN
:type hidden_layers_sizes: list of ints
:param hidden_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
"""
self.sigmoid_layers = []
self.rbm_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
# end-snippet-1
# The DBN is an MLP, for which all weights of intermediate
# layers are shared with a different RBM. We will first
# construct the DBN as a deep multilayer perceptron, and when
# constructing each sigmoidal layer we also construct an RBM
# that shares weights with that layer. During pretraining we
# will train these RBMs (which will lead to chainging the
# weights of the MLP as well) During finetuning we will finish
# training the DBN by doing stochastic 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 DBN 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 DBN. The visible
# biases in the RBM are parameters of those RBMs, but not
# of the DBN.
self.params.extend(sigmoid_layer.params)
# Construct an RBM that shared weights with this layer
rbm_layer = RBM(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,
hbias=sigmoid_layer.b)
self.rbm_layers.append(rbm_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)
# compute the cost for second phase of training, defined as the
# negative log likelihood of the logistic regression (output) layer
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, k):
'''Generates a list of functions, for performing one step of
gradient descent at a given layer. The function will require
as input the minibatch index, and to train an RBM 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 var. that contains all datapoints used
for training the RBM
:type batch_size: int
:param batch_size: size of a [mini]batch
:param k: number of Gibbs steps to do in CD-k / PCD-k
'''
# index to a [mini]batch
index = T.lscalar('index') # index to a minibatch
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 rbm in self.rbm_layers:
# get the cost and the updates list
# using CD-k here (persisent=None) for training each RBM.
# TODO: change cost function to reconstruction error
cost, updates = rbm.get_cost_updates(learning_rate,
persistent=None, k=k)
# compile the theano function
fn = theano.function(
inputs=[index, 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
]
}
)
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