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,
L1_reg=0,
L2_reg=0,
first_layer='grbm',
model=None):
"""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)
self.L1 = 0
self.L2_sqr = 0
assert self.n_layers > 0
if not theano_rng:
theano_rng = MRG_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[i - 1].output
if model is None:
W = None
b = None
else:
W = model[i * 2]
b = model[i * 2 + 1]
sigmoid_layer = HiddenLayer(rng=numpy_rng,
input=layer_input,
n_in=input_size,
n_out=hidden_layers_sizes[i],
W=W,
b=b,
activation=T.nnet.sigmoid)
# add the layer to our list of layers
self.sigmoid_layers.append(sigmoid_layer)
self.L1 += (abs(sigmoid_layer.W).sum())
self.L2_sqr += ((sigmoid_layer.W**2).sum())
# 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
if i == 0: # first layer GBRBM - dealing with continous value
if first_layer == 'grbm':
rbm_layer = GRBM(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)
if first_layer == 'rbm':
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)
# elif i == self.n_layers-1: # last layer GGRBM
# rbm_layer = GRBM(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)
else: # subsequence layers BBRBM - binary RBM to cope with regularization
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
if model is None:
W = None
b = None
else:
W = model[-2]
b = model[-1]
self.logLayer = LogisticRegression(
input=self.sigmoid_layers[-1].output,
n_in=hidden_layers_sizes[-1],
W=W,
b=b,
n_out=n_outs)
self.params.extend(self.logLayer.params)
self.L1 += (abs(self.logLayer.W).sum())
self.L2_sqr += ((self.logLayer.W**2).sum())
# 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) +
+L1_reg * self.L1 + L2_reg * self.L2_sqr)
# 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)
self.predprobs = self.logLayer.p_y_given_x
self.preds = self.logLayer.y_pred
def pretraining_functions(self, train_set_x, batch_size, cdk,
usepersistent):
'''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 cdk: number of Gibbs steps to do in CD-k / PCD-k
'''
# index to a [mini]batch
bc_idx = T.ivector('bc_idx') # 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
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
if usepersistent:
# init persisent chain
persistent_chain = theano.shared(numpy.zeros(
(batch_size, rbm.n_hidden), dtype=theano.config.floatX),
borrow=True)
cost, updates = rbm.get_cost_updates(
learning_rate, persistent=persistent_chain, k=cdk)
else:
cost, updates = rbm.get_cost_updates(learning_rate,
persistent=None,
k=cdk)
# compile the theano function
fn = theano.function(
inputs=[bc_idx,
theano.Param(learning_rate, default=0.1)],
outputs=cost,
updates=updates,
givens={self.x: train_set_x[bc_idx]})
# 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_train_batches = train_set_x.get_value(borrow=True).shape[0]
n_train_batches /= batch_size
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
bc_idx = T.ivector('bc_idx')
# compute the gradients with respect to the model parameters
#gparams = T.grad(self.finetune_cost, self.params)
gparams = [T.grad(self.finetune_cost, param) for param in self.params]
# compute list of fine-tuning updates
#updates = []
#for param, gparam in zip(self.params, gparams):
# updates.append((param, param - gparam * learning_rate))
updates = [(param, param - learning_rate * gparam)
for param, gparam in zip(self.params, gparams)]
train_fn = theano.function(inputs=[bc_idx],
outputs=self.finetune_cost,
updates=updates,
givens={
self.x: train_set_x[bc_idx],
self.y: train_set_y[bc_idx]
})
train_score_i = theano.function(
[index],
self.errors,
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 test set
def train_score():
return [train_score_i(i) for i in xrange(n_train_batches)]
# 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, train_score, valid_score, test_score
def evaluate_lenet5(learning_rate=0.1, n_epochs=200,
dataset='mnist.pkl.gz',
nkerns=[20,50],batch_size=500):
"""Demonstates lenet on MNIST dataset
"""
rng = numpy.random.RandomState(1234)
print('Loading Data'+'.'*20)
datasets = load_data(dataset)
trainSetX, trainSetY = datasets[0]
validSetX, validSetY = datasets[1]
testSetX, testSetY = datasets[2]
n_train_batches = trainSetX.get_value(borrow=True).shape[0] // batch_size
n_valid_batches = validSetX.get_value(borrow=True).shape[0] // batch_size
n_test_batches = testSetX.get_value(borrow=True).shape[0] // batch_size
print('Building Data'+'.'*20)
index = T.lscalar('index')
x = T.matrix('x')
y = T.ivector('y')
# Reshape matrix of rasterized images of shape (batch_size, 28*28)
# to a 4D tensor, compatible with our LeNetConvPoolLayer
layer0_input = x.reshape((batch_size,1,28,28))
# construct the first convolutional pooling layer
# filtering reduces the image size to (28-5+1,28-5+1) = (24, 24)
# maxpooling reduces this further to (24/2, 24/2) = (12, 12)
# 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)
layer0 = LeNetConvPoolLayer(
rng=rng,
input=layer0_input,
image_shape=(batch_size,1,28,28),
filter_shape=(nkerns[0],1,5,5),
poolsize=(2,2)
)
# construct the second convolutional pooling layer
# filtering reduces the image size to (12-5+1,12-5+1) = (8, 8)
# maxpooling reduces this further to (8/2, 8/2) = (4, 4)
# 4D output tensor is thus of shape (batch_size,nkerns[1],4,4)
layer1 = LeNetConvPoolLayer(
rng=rng,
input=layer0.output,
image_shape=(batch_size,nkerns[0],12,12),
filter_shape=(nkerns[1],nkerns[0],5,5),
poolsize=(2,2)
)
layer2_input = layer1.output.flatten(2)
layer2 = HiddenLayer(
rng=rng,
input=layer2_input,
n_in=nkerns[1]*4*4,
n_out=500,
activation=T.tanh
)
layer3 = LogisticRegression(input=layer2.output,n_in=500,n_out=10)
testModel = theano.function(
inputs=[index],
outputs=layer3.errors(y),
givens={
x:testSetX[index*batch_size:(index+1)*batch_size],
y:testSetY[index*batch_size:(index+1)*batch_size]
}
)
validModel = theano.function(
inputs=[index],
outputs=layer3.errors(y),
givens={
x:validSetX[index*batch_size:(index+1)*batch_size],
y:validSetY[index*batch_size:(index+1)*batch_size]
}
)
params = layer3.params+layer2.params+layer1.params+layer0.params
cost = layer3.negative_log_likelihood(y)
grads = T.grad(cost,params)
updates= [(param, param - learning_rate*grad)
for param,grad in zip(params,grads)
]
trainModel = theano.function(
inputs=[index],
outputs=cost,
updates=updates,
givens={
x:trainSetX[index*batch_size:(index+1)*batch_size],
y:trainSetY[index*batch_size:(index+1)*batch_size]
}
)
print('Training'+'.'*20)
patience = 10000
patience_increase = 2
improvement_threshold = 2
validation_frequence = min(n_train_batches, patience/2)
best_validation_loss = numpy.inf
best_iter = 0
test_score =0.
start_time = timeit.default_timer()
epoch = 0
done_looping = False
while (epoch < n_epochs) and (not done_looping):
epoch += 1
for mini_batch_index in range(n_train_batches):
iter = (epoch - 1) * n_train_batches + mini_batch_index
if iter % 100 == 0:
print('training @ iter = ' , iter)
cost_ij = trainModel(mini_batch_index)
if (iter + 1) % validation_frequence ==0:
validation_losses = [validModel(i) for i
in range(n_valid_batches)]
this_validation_losses = numpy.mean(validation_losses)
print('epoch %i, minibatch %i/%i, validation error %f %%' %
(epoch, mini_batch_index+1, n_train_batches,
this_validation_losses*100)
)
if this_validation_losses < best_validation_loss:
best_validation_loss = this_validation_losses
best_iter = iter
if this_validation_losses < best_validation_loss * \
improvement_threshold:
patience = max(patience, patience*patience_increase)
test_losses = [testModel(i) for i in range(n_test_batches)]
test_score = numpy.mean(test_losses)
print(' epoch %i, minibatch %i/%i, test error of'
'best model %f %%'%
(epoch, mini_batch_index+1, n_train_batches,
this_validation_losses*100)
)
if patience <= iter:
done_looping = True
break
endtime = timeit.default_timer()
print('Optimization complete.')
print('Best validation score of %f %% obtained at iteration %i, '
' with test performance %f %%' %
(best_validation_loss*100, best_iter+1, test_score*100.)
)
print('The code for file ' + os.path.split(__file__)[1]+
' ran for %.2fm' % (endtime - start_time)/60.
)
def evaluate_lenet5(learning_rate=0.01, n_epochs=200,
dataset='../testnn.mat',
nkerns=[20, 20], batch_size=100):
""" Demonstrates lenet on MNIST dataset
:type learning_rate: float
:param learning_rate: learning rate used (factor for the stochastic
gradient)
:type n_epochs: int
:param n_epochs: maximal number of epochs to run the optimizer
:type dataset: string
:param dataset: path to the dataset used for training /testing (MNIST here)
:type nkerns: list of ints
:param nkerns: number of kernels on each layer
"""
rng = numpy.random.RandomState(123)
# datasets = load_data(dataset)
datasets = loadmat(dataset=dataset, shuffle=shuffle, datasel=datasel, scaling=scaling, robust=robust)
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_valid_batches = valid_set_x.get_value(borrow=True).shape[0]
n_test_batches = test_set_x.get_value(borrow=True).shape[0]
n_train_batches /= batch_size
n_valid_batches /= batch_size
n_test_batches /= batch_size
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
# start-snippet-1
x = T.matrix('x') # the data is presented as rasterized images
y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# the below comments are examples of using this cnn to deal with MNIST with input feature size 784 = 28*28
# Reshape matrix of rasterized images of shape (batch_size, 28 * 28)
# to a 4D tensor, compatible with our LeNetConvPoolLayer
# (28, 28) is the size of MNIST images.
layer0_input = x.reshape((batch_size, 1, idim0_H, idim0_W))
# Construct the first convolutional pooling layer:
# filtering reduces the image size to (28-5+1 , 28-5+1) = (24, 24)
# maxpooling reduces this further to (24/2, 24/2) = (12, 12)
# 4D output tensor is thus of shape (batch_size, nkerns[0], 12, 12)
layer0 = LeNetConvPoolLayer(
rng,
input=layer0_input,
image_shape=(batch_size, 1, idim0_H, idim0_W),
filter_shape=(nkerns[0], 1, fdim0_H, fdim0_W),
poolsize=(pdim0_H, pdim0_W)
)
# Construct the second convolutional pooling layer
# filtering reduces the image size to (12-5+1, 12-5+1) = (8, 8)
# maxpooling reduces this further to (8/2, 8/2) = (4, 4)
# 4D output tensor is thus of shape (batch_size, nkerns[1], 4, 4)
layer1 = LeNetConvPoolLayer(
rng,
input=layer0.output,
image_shape=(batch_size, nkerns[0], idim1_H, idim1_W),
filter_shape=(nkerns[1], nkerns[0], fdim1_H, fdim1_W),
poolsize=(pdim1_H, pdim1_W)
)
# the HiddenLayer being fully-connected, it operates on 2D matrices of
# shape (batch_size, num_pixels) (i.e matrix of rasterized images).
# This will generate a matrix of shape (batch_size, nkerns[1] * 4 * 4),
# or (500, 50 * 4 * 4) = (500, 800) with the default values.
layer2_input = layer1.output.flatten(2)
# construct a fully-connected sigmoidal layer
layer2 = HiddenLayer(
rng,
input=layer2_input,
n_in=nkerns[1] * idim2_H * idim2_W,
n_out=fdim2,
activation=T.tanh
)
# classify the values of the fully-connected sigmoidal layer
nclass = max(train_set_y.eval()) + 1
layer3 = LogisticRegression(input=layer2.output, n_in=fdim2, n_out=nclass)
# the cost we minimize during training is the NLL of the model
cost = layer3.negative_log_likelihood(y)
# create a function to compute the mistakes that are made by the model
test_model = theano.function(
[index],
layer3.errors(y),
givens={
x: test_set_x[index * batch_size: (index + 1) * batch_size],
y: test_set_y[index * batch_size: (index + 1) * batch_size]
}
)
validate_model = theano.function(
[index],
layer3.errors(y),
givens={
x: valid_set_x[index * batch_size: (index + 1) * batch_size],
y: valid_set_y[index * batch_size: (index + 1) * batch_size]
}
)
train_score = theano.function(
[index],
layer3.errors(y),
givens={
x: train_set_x[index * batch_size: (index + 1) * batch_size],
y: train_set_y[index * batch_size: (index + 1) * batch_size]
}
)
# create a list of all model parameters to be fit by gradient descent
params = layer3.params + layer2.params + layer1.params + layer0.params
# create a list of gradients for all model parameters
grads = T.grad(cost, params)
# train_model is a function that updates the model parameters by
# SGD Since this model has many parameters, it would be tedious to
# manually create an update rule for each model parameter. We thus
# create the updates list by automatically looping over all
# (params[i], grads[i]) pairs.
updates = [
(param_i, param_i - learning_rate * grad_i)
for param_i, grad_i in zip(params, grads)
]
train_model = theano.function(
[index],
cost,
updates=updates,
givens={
x: train_set_x[index * batch_size: (index + 1) * batch_size],
y: train_set_y[index * batch_size: (index + 1) * batch_size]
}
)
# end-snippet-1
###############
# TRAIN MODEL #
###############
print '... training'
# 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_validation_loss = numpy.inf
best_iter = 0
test_score = 0.
start_time = timeit.default_timer()
epoch = 0
done_looping = False
while (epoch < n_epochs):
if earlystop and done_looping:
print 'early-stopping'
break
epoch = epoch + 1
for minibatch_index in xrange(n_train_batches):
iter = (epoch - 1) * n_train_batches + minibatch_index
if iter % 100 == 0:
print 'training @ iter = ', iter
cost_ij = train_model(minibatch_index)
if (iter + 1) % validation_frequency == 0:
# compute zero-one loss on validation set
validation_losses = [validate_model(i) for i
in xrange(n_valid_batches)]
training_losses = [train_score(i) for i
in xrange(n_valid_batches)]
this_validation_loss = numpy.mean(validation_losses)
this_training_loss = numpy.mean(training_losses)
print('epoch %i, minibatch %i/%i, training error %f %%' %
(epoch, minibatch_index + 1, n_train_batches,
this_training_loss * 100.))
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(i)
for i in xrange(n_test_batches)
]
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
if earlystop:
break
end_time = timeit.default_timer()
print('Optimization complete.')
print('Best validation score of %f %% obtained at iteration %i, '
'with test performance %f %%' %
(best_validation_loss * 100., best_iter + 1, test_score * 100.))
print >> sys.stderr, ('The code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.))
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, L1_reg=0, L2_reg=0, first_layer='grbm',model=None):
"""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)
self.L1 = 0
self.L2_sqr = 0
assert self.n_layers > 0
if not theano_rng:
theano_rng = MRG_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[i - 1].output
if model is None:
W = None
b = None
else:
W = model[i*2]
b = model[i*2 + 1]
sigmoid_layer = HiddenLayer(rng=numpy_rng,
input=layer_input,
n_in=input_size,
n_out=hidden_layers_sizes[i],
W = W,
b = b,
activation=T.nnet.sigmoid)
# add the layer to our list of layers
self.sigmoid_layers.append(sigmoid_layer)
self.L1 += (abs(sigmoid_layer.W).sum())
self.L2_sqr += ((sigmoid_layer.W ** 2).sum())
# 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
if i == 0: # first layer GBRBM - dealing with continous value
if first_layer == 'grbm':
rbm_layer = GRBM(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)
if first_layer == 'rbm':
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)
# elif i == self.n_layers-1: # last layer GGRBM
# rbm_layer = GRBM(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)
else: # subsequence layers BBRBM - binary RBM to cope with regularization
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
if model is None:
W = None
b = None
else:
W = model[-2]
b = model[-1]
self.logLayer = LogisticRegression(
input=self.sigmoid_layers[-1].output,
n_in=hidden_layers_sizes[-1],
W = W,
b = b,
n_out=n_outs)
self.params.extend(self.logLayer.params)
self.L1 += (abs(self.logLayer.W).sum())
self.L2_sqr += ((self.logLayer.W ** 2).sum())
# 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) +
+ L1_reg * self.L1
+ L2_reg * self.L2_sqr
)
# 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)
self.predprobs = self.logLayer.p_y_given_x
self.preds = self.logLayer.y_pred
def pretraining_functions(self, train_set_x, batch_size, cdk, usepersistent):
'''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 cdk: 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
if usepersistent:
# init persisent chain
persistent_chain = theano.shared(numpy.zeros((batch_size, rbm.n_hidden),
dtype=theano.config.floatX),
borrow=True)
cost, updates = rbm.get_cost_updates(learning_rate,
persistent=persistent_chain, k=cdk)
else:
cost, updates = rbm.get_cost_updates(learning_rate,
persistent=None, k=cdk)
# 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_train_batches = train_set_x.get_value(borrow=True).shape[0]
n_train_batches /= batch_size
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)
gparams = [T.grad(self.finetune_cost, param) for param in self.params]
# compute list of fine-tuning updates
#updates = []
#for param, gparam in zip(self.params, gparams):
# updates.append((param, param - gparam * learning_rate))
updates = [
(param, param - learning_rate * gparam)
for param, gparam in zip(self.params, gparams)
]
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
]
}
)
train_score_i = theano.function(
[index],
self.errors,
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 test set
def train_score():
return [train_score_i(i) for i in xrange(n_train_batches)]
# 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, train_score, valid_score, test_score
def sgd_optimization_mnist(learning_rate=0.13,
n_epochs=1000,
dataset='data/mnist.pkl.gz',
batch_size=600):
training_set, validation_set, testing_set, = data_loader.load(dataset)
training_set_x, training_set_y = training_set
validation_set_x, validation_set_y = validation_set
testing_set_x, testing_set_y = testing_set
# compute number of minibatches for training, validation and testing
n_train_batches = training_set_x.get_value(
borrow=True).shape[0] / batch_size
n_valid_batches = validation_set_x.get_value(
borrow=True).shape[0] / batch_size
n_test_batches = testing_set_x.get_value(borrow=True).shape[0] / batch_size
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# allocate symbolic variables for the data
index = tensor.lscalar()
# generate symbolic variables for input (x and y represent a
# minibatch)
x = tensor.matrix('x')
y = tensor.ivector('y')
classifier = LogisticRegression(input=x, n_in=28 * 28, n_out=10)
cost = classifier.negative_log_likelihood(y)
# compiling a Theano function that computes the mistakes that are made by
# the model on a minibatch
test_model = theano.function(
inputs=[index],
outputs=classifier.errors(y),
givens={
x: testing_set_x[index * batch_size:(index + 1) * batch_size],
y: testing_set_y[index * batch_size:(index + 1) * batch_size]
})
validate_model = theano.function(
inputs=[index],
outputs=classifier.errors(y),
givens={
x: validation_set_x[index * batch_size:(index + 1) * batch_size],
y: validation_set_y[index * batch_size:(index + 1) * batch_size]
})
# compute the gradient of cost with respect to theta = (W,b)
g_W = tensor.grad(cost=cost, wrt=classifier.W)
g_b = tensor.grad(cost=cost, wrt=classifier.b)
# update the parameters of the model
updates = [(classifier.W, classifier.W - learning_rate * g_W),
(classifier.b, classifier.b - learning_rate * g_b)]
# compiling a Theano function `train_model` that returns the cost, but in
# the same time updates the parameter of the model based on the rules
# defined in `updates`
train_model = theano.function(
inputs=[index],
outputs=cost,
updates=updates,
givens={
x: training_set_x[index * batch_size:(index + 1) * batch_size],
y: training_set_y[index * batch_size:(index + 1) * batch_size]
})
###############
# TRAIN MODEL #
###############
print '... training the model'
# early-stopping parameters
patience = 5000 # 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 = 5 * n_train_batches # requency of training
best_validation_loss = numpy.inf
test_score = 0.
start_time = timeit.default_timer()
done_looping = False
epoch = 0
while (epoch < n_epochs) and (not done_looping):
for minibatch_index in xrange(n_train_batches):
minibatch_avg_cost = train_model(minibatch_index)
# iter: number of minibatches used)
iter = epoch * n_train_batches + minibatch_index
if (iter + 1) % validation_frequency == 0:
# compute zero-one loss on validation set
validation_losses = [
validate_model(i) for i in xrange(n_valid_batches)
]
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)
# update best_validation_loss
best_validation_loss = this_validation_loss
# test it on the test set
test_losses = [
test_model(i) for i in xrange(n_test_batches)
]
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.))
# save the best model
with open('best_model.pkl', 'w') as f:
cPickle.dump(classifier, f)
if patience <= iter:
done_looping = True
break
epoch = epoch + 1
end_time = timeit.default_timer()
print(('Optimization complete with best validation score of %f %%,'
'with test performance %f %%') %
(best_validation_loss * 100., test_score * 100.))
print 'The code run for %d epochs, with %f epochs/sec' % (
epoch, 1. * epoch / (end_time - start_time))
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, nkerns=[20, 50]):
"""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 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
"""
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
batch_size=500
# 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.
rng = numpy.random.RandomState(23455)
self.layer0_input = self.x.reshape((batch_size, 1, 28, 28))
# Construct the first convolutional pooling layer:
# filtering reduces the image size to (28-5+1,28-5+1)=(24,24)
# maxpooling reduces this further to (24/2,24/2) = (12,12)
# 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)
self.layer0 = LeNetConvPoolLayer(rng, input=self.layer0_input,
image_shape=(batch_size, 1, 28, 28),
filter_shape=(nkerns[0], 1, 5, 5), poolsize=(2, 2))
# Construct the second convolutional pooling layer
# filtering reduces the image size to (12-5+1,12-5+1)=(8,8)
# maxpooling reduces this further to (8/2,8/2) = (4,4)
# 4D output tensor is thus of shape (nkerns[0],nkerns[1],4,4)
self.layer1 = LeNetConvPoolLayer(rng, input=self.layer0.output,
image_shape=(batch_size, nkerns[0], 12, 12),
filter_shape=(nkerns[1], nkerns[0], 5, 5), poolsize=(2, 2))
# the TanhLayer being fully-connected, it operates on 2D matrices of
# shape (batch_size,num_pixels) (i.e matrix of rasterized images).
# This will generate a matrix of shape (20,32*4*4) = (20,512)
self.layer2_input = self.layer1.output.flatten(2)
self.layer2=HiddenLayer(rng,input=self.layer2_input,n_in=nkerns[1]*4*4,n_out=500,activation=T.tanh)
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 = 500
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.layer2.output
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
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
# end-snippet-1
# 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
# start-snippet-2
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)
# end-snippet-2
# 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
# 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 = [
(param, param - gparam * learning_rate)
for param, gparam in zip(self.params, gparams)
]
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
# In[ ]:
# Actual training #
# Actual training begins here
minibatch_avg_cost = 0
for j in xrange(300):
for i in xrange(n_train_batches):
minibatch_avg_cost = train(i)
print 'iteration ',j,' : cost : ', minibatch_avg_cost
# In[ ]:
# testing
test = theano.function(inputs = [index],
outputs = layer3_o.errors(y),
givens = { x : test_set_x[index*batch_size : (index +1)*batch_size],
y : test_set_y[index*batch_size : (index +1)*batch_size]
}
)
error_sum = 0.0
for i in xrange(n_test_batches):
error_sum += test(i)
print 'avg_error : ',error_sum/n_test_batches
# In[ ]:
# visualize feature maps in convolnet
visual = theano.function(inputs=[index],
outputs = [layer3_o.errors(y),layer0.output],
def test_cnn(trainpath,
trainlist,
validset,
dumppath,
learning_rate=0.01,
n_epochs=200,
batch_size=100,
earlystop=True):
"""
:type learning_rate: float
:param learning_rate: learning rate used (factor for the stochastic
gradient)
:type n_epochs: int
:param n_epochs: maximal number of epochs to run the optimizer
:type dataset: string
:param dataset: path to the dataset used for training /testing (MNIST here)
:type nkerns: list of ints
:param nkerns: number of kernels on each layer
"""
rng = numpy.random.RandomState(123)
# datasets = load_data(dataset)
datasets = loadmat(trainpath=trainpath,
trainlist=trainlist,
validset=validset,
shuffle=shuffle,
datasel=datasel,
scaling=scaling,
robust=robust)
train_set_x, train_set_y = datasets[0]
valid_set_x, valid_set_y = datasets[1]
# compute number of minibatches for training, validation and testing
n_train_batches = train_set_x.get_value(borrow=True).shape[0]
n_valid_batches = valid_set_x.get_value(borrow=True).shape[0]
n_train_batches /= batch_size
n_valid_batches /= batch_size
# allocate symbolic variables for the data
index = T.lscalar() # index to a [mini]batch
# start-snippet-1
x = T.matrix('x') # the data is presented as rasterized images
y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# H - height; W - width
# when the input is note salience matrix
# idim0_H = 42
# idim0_W = 36
# fdim0_H = 6
# fdim0_W = 6
# when the input is chromagram
idim0_H = 12
idim0_W = 12
fdim0_H = 2
fdim0_W = 2
pdim0_H = 2
pdim0_W = 2
idim1_H = (idim0_H - fdim0_H + 1) / pdim0_H
idim1_W = (idim0_W - fdim0_W + 1) / pdim0_W
fdim1_H = 2
fdim1_W = 2
pdim1_H = 2
pdim1_W = 2
idim2_H = (idim1_H - fdim1_H + 1) / pdim1_H
idim2_W = (idim1_W - fdim1_W + 1) / pdim1_W
fdim2 = 800
nkerns = [20, 20]
# the below comments are examples of using this cnn to deal with chromagram with input feature size 144 = 12*12
# Reshape matrix of rasterized images of shape (batch_size, 12 * 12)
# to a 4D tensor, compatible with our ConvPoolLayer
# (12, 12) is the size of MNIST images.
layer0_input = x.reshape((batch_size, 1, idim0_H, idim0_W))
# Construct the first convolutional pooling layer:
# filtering reduces the image size to (12-2+1 , 12-2+1) = (11, 11)
# maxpooling reduces this further to (11/2, 11/2) = (5, 5)
# 4D output tensor is thus of shape (batch_size, nkerns[0], 5, 5)
layer0 = ConvPoolLayer(rng,
input=layer0_input,
input_shape=(batch_size, 1, idim0_H, idim0_W),
filter_shape=(nkerns[0], 1, fdim0_H, fdim0_W),
poolsize=(pdim0_H, pdim0_W))
# Construct the second convolutional pooling layer
# filtering reduces the image size to (5-2+1, 5-2+1) = (4, 4)
# maxpooling reduces this further to (4/2, 4/2) = (2, 2)
# 4D output tensor is thus of shape (batch_size, nkerns[1], 2, 2)
layer1 = ConvPoolLayer(rng,
input=layer0.output,
input_shape=(batch_size, nkerns[0], idim1_H,
idim1_W),
filter_shape=(nkerns[1], nkerns[0], fdim1_H,
fdim1_W),
poolsize=(pdim1_H, pdim1_W))
# the HiddenLayer being fully-connected, it operates on 2D matrices of
# shape (batch_size, num_pixels) (i.e matrix of rasterized images).
# This will generate a matrix of shape (batch_size, nkerns[1] * 2 * 2),
# or (500, 50 * 4 * 4) = (500, 800) with the default values.
layer2_input = layer1.output.flatten(2)
# construct a fully-connected sigmoidal layer
layer2 = HiddenLayer(rng,
input=layer2_input,
n_in=nkerns[1] * idim2_H * idim2_W,
n_out=fdim2,
activation=T.nnet.relu)
# classify the values of the fully-connected sigmoidal layer
nclass = max(train_set_y.eval()) + 1
layer3 = LogisticRegression(input=layer2.output, n_in=fdim2, n_out=nclass)
# the cost we minimize during training is the NLL of the model
cost = layer3.negative_log_likelihood(y)
# create a function to compute the mistakes that are made by the model
validate_model = theano.function(
[index],
layer3.errors(y),
givens={
x: valid_set_x[index * batch_size:(index + 1) * batch_size],
y: valid_set_y[index * batch_size:(index + 1) * batch_size]
})
train_score = theano.function(
[index],
layer3.errors(y),
givens={
x: train_set_x[index * batch_size:(index + 1) * batch_size],
y: train_set_y[index * batch_size:(index + 1) * batch_size]
})
# create a list of all model parameters to be fit by gradient descent
params = layer3.params + layer2.params + layer1.params + layer0.params
# create a list of gradients for all model parameters
grads = T.grad(cost, params)
# train_model is a function that updates the model parameters by
# SGD Since this model has many parameters, it would be tedious to
# manually create an update rule for each model parameter. We thus
# create the updates list by automatically looping over all
# (params[i], grads[i]) pairs.
updates = [(param_i, param_i - learning_rate * grad_i)
for param_i, grad_i in zip(params, grads)]
train_model = theano.function(
[index],
cost,
updates=updates,
givens={
x: train_set_x[index * batch_size:(index + 1) * batch_size],
y: train_set_y[index * batch_size:(index + 1) * batch_size]
})
# end-snippet-1
###############
# TRAIN MODEL #
###############
print '... training'
# 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 = 0.996 # 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_validation_loss = numpy.inf
best_iter = 0
training_history = []
start_time = timeit.default_timer()
epoch = 0
done_looping = False
while (epoch < n_epochs):
if earlystop and done_looping:
print 'early-stopping'
break
epoch = epoch + 1
for minibatch_index in xrange(n_train_batches):
iter = (epoch - 1) * n_train_batches + minibatch_index
cost_ij = train_model(minibatch_index)
if (iter + 1) % validation_frequency == 0:
# compute zero-one loss on validation set
validation_losses = [
validate_model(i) for i in xrange(n_valid_batches)
]
#training_losses = [train_score(i) for i in xrange(n_valid_batches)]
this_validation_loss = numpy.mean(validation_losses)
#this_training_loss = numpy.mean(training_losses)
#training_history.append([iter,this_training_loss,this_validation_loss])
training_history.append([iter, this_validation_loss])
# print('epoch %i, minibatch %i/%i, training error %f %%' %
# (epoch, minibatch_index + 1, n_train_batches,
# this_training_loss * 100.))
print('epoch %i, minibatch %i/%i, validation error %f %%' %
(epoch, minibatch_index + 1, n_train_batches,
this_validation_loss * 100.))
print('iter = %d' % iter)
print('patience = %d' % patience)
# 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)
numpy.savez(dumppath,
model=params,
training_history=training_history,
best_validation_loss=best_validation_loss)
# save best validation score and iteration number
best_validation_loss = this_validation_loss
best_iter = iter
print('best_validation_loss %f' % best_validation_loss)
if patience <= iter:
done_looping = True
if earlystop:
break
end_time = timeit.default_timer()
# final save
numpy.savez(dumppath,
model=params,
training_history=training_history,
best_validation_loss=best_validation_loss)
print(('Optimization complete with best validation score of %f %%, '
'obtained at iteration %i, ') %
(best_validation_loss * 100., best_iter + 1))
print >> sys.stderr, ('The fine tuning code for file ' +
os.path.split(__file__)[1] + ' ran for %.2fm' %
((end_time - start_time) / 60.))
def evaluate_lenet5(learning_rate=0.1,
n_epochs=200,
dataset='../data/mnist.pkl.gz',
nkerns=[20, 50],
batch_size=500):
""" Demonstrates lenet on MNIST dataset
:type learning_rate: float
:param learning_rate: learning rate used (factor for the stochastic
gradient)
:type n_epochs: int
:param n_epochs: maximal number of epochs to run the optimizer
:type dataset: string
:param dataset: path to the dataset used for training /testing (MNIST here)
:type nkerns: list of ints
:param nkerns: number of kernels on each layer
"""
rng = numpy.random.RandomState(23455)
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_valid_batches = valid_set_x.get_value(borrow=True).shape[0]
n_test_batches = test_set_x.get_value(borrow=True).shape[0]
n_train_batches /= batch_size
n_valid_batches /= batch_size
n_test_batches /= 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
y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
ishape = (28, 28) # this is the size of MNIST images
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# Reshape matrix of rasterized images of shape (batch_size,28*28)
# to a 4D tensor, compatible with our LeNetConvPoolLayer
layer0_input = x.reshape((batch_size, 1, 28, 28))
# Construct the first convolutional pooling layer:
# filtering reduces the image size to (28-5+1,28-5+1)=(24,24)
# maxpooling reduces this further to (24/2,24/2) = (12,12)
# 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)
layer0 = LeNetConvPoolLayer(rng,
input=layer0_input,
image_shape=(batch_size, 1, 28, 28),
filter_shape=(nkerns[0], 1, 5, 5),
poolsize=(2, 2))
# Construct the second convolutional pooling layer
# filtering reduces the image size to (12-5+1,12-5+1)=(8,8)
# maxpooling reduces this further to (8/2,8/2) = (4,4)
# 4D output tensor is thus of shape (nkerns[0],nkerns[1],4,4)
layer1 = LeNetConvPoolLayer(rng,
input=layer0.output,
image_shape=(batch_size, nkerns[0], 12, 12),
filter_shape=(nkerns[1], nkerns[0], 5, 5),
poolsize=(2, 2))
# the TanhLayer being fully-connected, it operates on 2D matrices of
# shape (batch_size,num_pixels) (i.e matrix of rasterized images).
# This will generate a matrix of shape (20,32*4*4) = (20,512)
layer2_input = layer1.output.flatten(2)
# construct a fully-connected sigmoidal layer
layer2 = HiddenLayer(rng,
input=layer2_input,
n_in=nkerns[1] * 4 * 4,
n_out=500,
activation=T.tanh)
# classify the values of the fully-connected sigmoidal layer
layer3 = LogisticRegression(input=layer2.output, n_in=500, n_out=10)
# the cost we minimize during training is the NLL of the model
cost = layer3.negative_log_likelihood(y)
# create a function to compute the mistakes that are made by the model
test_model = theano.function(
[index],
layer3.errors(y),
givens={
x: test_set_x[index * batch_size:(index + 1) * batch_size],
y: test_set_y[index * batch_size:(index + 1) * batch_size]
})
validate_model = theano.function(
[index],
layer3.errors(y),
givens={
x: valid_set_x[index * batch_size:(index + 1) * batch_size],
y: valid_set_y[index * batch_size:(index + 1) * batch_size]
})
# create a list of all model parameters to be fit by gradient descent
params = layer3.params + layer2.params + layer1.params + layer0.params
# create a list of gradients for all model parameters
grads = T.grad(cost, params)
# train_model is a function that updates the model parameters by
# SGD Since this model has many parameters, it would be tedious to
# manually create an update rule for each model parameter. We thus
# create the updates list by automatically looping over all
# (params[i],grads[i]) pairs.
updates = []
for param_i, grad_i in zip(params, grads):
updates.append((param_i, param_i - learning_rate * grad_i))
train_model = theano.function(
[index],
cost,
updates=updates,
givens={
x: train_set_x[index * batch_size:(index + 1) * batch_size],
y: train_set_y[index * batch_size:(index + 1) * batch_size]
})
###############
# TRAIN MODEL #
###############
print '... training'
# 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 = numpy.inf
best_iter = 0
test_score = 0.
start_time = time.clock()
epoch = 0
done_looping = False
while (epoch < n_epochs) and (not done_looping):
epoch = epoch + 1
for minibatch_index in xrange(n_train_batches):
iter = (epoch - 1) * n_train_batches + minibatch_index
if iter % 100 == 0:
print 'training @ iter = ', iter
cost_ij = train_model(minibatch_index)
if (iter + 1) % validation_frequency == 0:
# compute zero-one loss on validation set
validation_losses = [
validate_model(i) for i in xrange(n_valid_batches)
]
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(i) for i in xrange(n_test_batches)
]
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.')
print('Best validation score of %f %% obtained at iteration %i,'\
'with test performance %f %%' %
(best_validation_loss * 100., best_iter + 1, test_score * 100.))
print >> sys.stderr, ('The code for file ' + os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.))
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, n_ins, hidden_layers_sizes, corruption_levels=[0.1, 0.1], theano_rng=None, n_outs=7):
""" 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)
self.n_ins = n_ins
self.n_outs = n_outs
# allocate symbolic variables for the data
self.x = T.matrix("x") # the data is presented as rasterized images
self.y = T.iscalar("y") # the labels are presented as 1D vector of
# [int] labels
assert self.n_layers > 0
if not theano_rng:
theano_rng = RandomStreams(numpy_rng.randint(2 ** 30))
# end-snippet-1
# 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
# start-snippet-2
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.append(sigmoid_layer.theta)
# 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],
theta=sigmoid_layer.theta,
)
self.dA_layers.append(dA_layer)
# end-snippet-2
# 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.append(self.logLayer.params)
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)
self.predict = self.logLayer.predict()
class DBN(object):
def __init__(self,
numpy_rng,
theano_rng=None,
n_ins=784,
hidden_layers_sizes=[500, 500],
n_outs=10):
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 = theano_rng = RandomStreams(numpy_rng.randint(2**30))
self.x = T.matrix('x')
self.y = T.ivector('y')
for i in range(self.n_layers):
if i == 0:
input_size = n_ins
else:
input_size = hidden_layers_sizes[i - 1]
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)
self.sigmoid_layers.append(sigmoid_layer)
self.params.extend(sigmoid_layer.params)
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)
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)
self.finetune_cost = self.logLayer.negative_log_likehood(self.y)
self.errors = self.logLayer.errors(self.y)
def pretraining_functions(self, train_set_x, batch_size, k):
index = T.lscalar('index')
learning_rate = T.scalar('lr')
batch_begin = index * batch_size
batch_end = batch_begin + batch_size
pretrain_fns = []
for rbm in self.rbm_layers:
cost, updates = rbm.get_cost_updates(learning_rate,
persistent=None,
k=k)
fn = theano.function(
inputs=[index, theano.In(learning_rate, value=0.1)],
outputs=cost,
updates=updates,
givens={self.x: train_set_x[batch_begin:batch_end]})
pretrain_fns.append(fn)
return pretrain_fns
def build_finetune_functions(self, datasets, batch_size, learning_rate):
(train_set_x, train_set_y) = datasets[0]
(test_set_x, test_set_y) = datasets[1]
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
gparams = T.grad(self.finetune_cost, self.params)
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]
})
def test_score():
return [test_score_i(i) for i in range(n_test_batches)]
valid_score = None
return train_fn, valid_score, test_score
def predict(self):
test_set = logistic.load_my_test_data()
test_set_x = test_set.get_value()
predict_model = theano.function(inputs=[self.x],
outputs=self.logLayer.y_pred)
predicted_values = predict_model(test_set_x)
ids = numpy.arange(predicted_values.shape[0] + 1)
print ids.dtype
print predicted_values
df = pd.DataFrame({"ImageId": ids[1:], "Label": predicted_values})
print df
df.to_csv('submission.csv', index=False, index_label=True)
class SdA(object):
"""Stacked denoising autoencoder class (sdA)
A stacked denoising autoencoder mode 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_in=784,
hidden_layers_sizes=[500, 500], n_out=10,corruption_levels=[0.,0.1]):
"""This class is made to support a variable number of layers.
:type theano_rng: theano.tensor.shared_randomstream.RandomSteam
:param theano_rng: Thenao random generator used to draw initial weights
:type n_in: int
:param n_in: dimension of the input to the sdA
:type hidden_layers_sizes: list of ints
:param hidden_layers_sizes: intermediate layers size, must contain
at least one value
:type n_out: int
:param n_out: 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.dA_layers will store the denoising autoencoder associated
# with the layers of the MLP
self.dA_layers = []
# self.sigmoid_layers will store the sigmoid layers of the MLP facade
self.sigmoid_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 rasteried images
self.y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
#
# Construct self.n_layers sigmoid layers and self.n_layers denoising
# layersm where self.n_layers is the depth of our model
#
for i in range(self.n_layers):
# construct a sigmoid layer
#
# the size of the input is ethier the number of the hidden units of
# the layer below or the input size if we are on the first layer.
# the input of the layer has the same situation
if i == 0:
input_size = n_in
layer_input = self.x
else:
input_size = hidden_layers_sizes[i-1]
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 layer
self.sigmoid_layers.append(sigmoid_layer)
# ??? the parameters of the sigmoid layers are paremeters of the
# sdA, the visible bias in the dA are parameters of those
# dA, but not the sdA. So we do not add the dA_layer's (below)
# bvis to self.params.
self.params.extend(sigmoid_layer.params)
# construct a denoising autoencoder that shared weights with this
# sigmoid_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)
#
# Construct 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_out
)
self.params.extend(self.logLayer.params)
#
# Construct a function that impletements one step of finetuning
#
# 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, trainSetX, batch_size):
''' Generates a list of functions, each of them implementing one
step in training 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 trainSetX: theano.tensor.TensorType
:param trainSetX: Shared variable that contains all datapoints used
for training the dA
:type batch_size: int
:param batch_size: size of a minibatch
'''
index = T.lscalar('index')
corruption_level = T.scalar('corruption')
learning_rate = T.scalar('lr')
batch_begin = index * batch_size
batch_end = batch_begin + batch_size
pretrain_fns = []
for dA in self.dA_layers:
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: trainSetX[batch_begin:batch_end]
}
)
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 theano.tensor.TensorType
:param datasets: It is a list that contain all the datasets;
that as 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 labels
:type batch_size: int
:param batch_size: learning_rate used during finetuns stage
:type learning_rate: float
:param learning_rate: learning_rate used during finetune stage
'''
trainSetX, trainSetY = datasets[0]
validSetX, validSetY = datasets[1]
testSetX, testSetY = datasets[2]
n_valid_batches = validSetX.get_value(borrow=True).shape[0] // batch_size
n_test_batches = testSetX.get_value(borrow=True).shape[0] // batch_size
index = T.lscalar('index')
batch_begin = index * batch_size
batch_end = batch_begin + batch_size
gparams = T.grad(self.finetune_cost, self.params)
updates = [(param, param - learning_rate*gparam)
for param, gparam in zip(self.params, gparams)]
train_fn = theano.function(
inputs=[index],
outputs=self.finetune_cost,
updates=updates,
givens={
self.x :trainSetX[batch_begin:batch_end],
self.Y :trainSetY[batch_begin:batch_end]
},
name='train'
)
valid_score_i = theano.function(
inputs=[index],
outputs=self.errors,
givens={
self.x :validSetX[batch_begin:batch_end],
self.Y :validSetY[batch_begin:batch_end]
},
name='valid'
)
test_score_i = theano.function(
inputs=[index],
outputs=self.errors,
givens={
self.x :testSetX[batch_begin:batch_end],
self.Y :testSetY[batch_begin:batch_end]
},
name='test'
)
def valid_score():
return [valid_score_i(i) for i in range(n_valid_batches)]
def test_score():
return [test_score_i(i) for i in range(n_test_batches)]
return train_fn, valid_score, test_score
def sgd_optimization_mnist(learning_rate=0.13, n_epochs=1000,
dataset='data/mnist.pkl.gz',
batch_size=600):
training_set, validation_set, testing_set, = data_loader.load(dataset)
training_set_x , training_set_y = training_set
validation_set_x, validation_set_y = validation_set
testing_set_x , testing_set_y = testing_set
# compute number of minibatches for training, validation and testing
n_train_batches = training_set_x.get_value(borrow=True).shape[0] / batch_size
n_valid_batches = validation_set_x.get_value(borrow=True).shape[0] / batch_size
n_test_batches = testing_set_x.get_value(borrow=True).shape[0] / batch_size
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
# allocate symbolic variables for the data
index = tensor.lscalar()
# generate symbolic variables for input (x and y represent a
# minibatch)
x = tensor.matrix('x')
y = tensor.ivector('y')
classifier = LogisticRegression(input=x, n_in=28 * 28, n_out=10)
cost = classifier.negative_log_likelihood(y)
# compiling a Theano function that computes the mistakes that are made by
# the model on a minibatch
test_model = theano.function(
inputs=[index],
outputs=classifier.errors(y),
givens={
x: testing_set_x[index * batch_size: (index + 1) * batch_size],
y: testing_set_y[index * batch_size: (index + 1) * batch_size]
}
)
validate_model = theano.function(
inputs=[index],
outputs=classifier.errors(y),
givens={
x: validation_set_x[index * batch_size: (index + 1) * batch_size],
y: validation_set_y[index * batch_size: (index + 1) * batch_size]
}
)
# compute the gradient of cost with respect to theta = (W,b)
g_W = tensor.grad(cost=cost, wrt=classifier.W)
g_b = tensor.grad(cost=cost, wrt=classifier.b)
# update the parameters of the model
updates = [(classifier.W, classifier.W - learning_rate * g_W),
(classifier.b, classifier.b - learning_rate * g_b)]
# compiling a Theano function `train_model` that returns the cost, but in
# the same time updates the parameter of the model based on the rules
# defined in `updates`
train_model = theano.function(
inputs=[index],
outputs=cost,
updates=updates,
givens={
x: training_set_x[index * batch_size: (index + 1) * batch_size],
y: training_set_y[index * batch_size: (index + 1) * batch_size]
}
)
###############
# TRAIN MODEL #
###############
print '... training the model'
# early-stopping parameters
patience = 5000 # 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 = 5 * n_train_batches # requency of training
best_validation_loss = numpy.inf
test_score = 0.
start_time = timeit.default_timer()
done_looping = False
epoch = 0
while (epoch < n_epochs) and (not done_looping):
for minibatch_index in xrange(n_train_batches):
minibatch_avg_cost = train_model(minibatch_index)
# iter: number of minibatches used)
iter = epoch * n_train_batches + minibatch_index
if (iter + 1) % validation_frequency == 0:
# compute zero-one loss on validation set
validation_losses = [validate_model(i) for i in xrange(n_valid_batches)]
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)
# update best_validation_loss
best_validation_loss = this_validation_loss
# test it on the test set
test_losses = [test_model(i) for i in xrange(n_test_batches)]
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.
)
)
# save the best model
with open('best_model.pkl', 'w') as f:
cPickle.dump(classifier, f)
if patience <= iter:
done_looping = True
break
epoch = epoch + 1
end_time = timeit.default_timer()
print(
(
'Optimization complete with best validation score of %f %%,'
'with test performance %f %%'
)
% (best_validation_loss * 100., test_score * 100.)
)
print 'The code run for %d epochs, with %f epochs/sec' % (
epoch, 1. * epoch / (end_time - start_time))
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,
nkerns=[20, 50]):
"""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 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
"""
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
batch_size = 500
# 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.
rng = numpy.random.RandomState(23455)
self.layer0_input = self.x.reshape((batch_size, 1, 28, 28))
# Construct the first convolutional pooling layer:
# filtering reduces the image size to (28-5+1,28-5+1)=(24,24)
# maxpooling reduces this further to (24/2,24/2) = (12,12)
# 4D output tensor is thus of shape (batch_size,nkerns[0],12,12)
self.layer0 = LeNetConvPoolLayer(rng,
input=self.layer0_input,
image_shape=(batch_size, 1, 28, 28),
filter_shape=(nkerns[0], 1, 5, 5),
poolsize=(2, 2))
# Construct the second convolutional pooling layer
# filtering reduces the image size to (12-5+1,12-5+1)=(8,8)
# maxpooling reduces this further to (8/2,8/2) = (4,4)
# 4D output tensor is thus of shape (nkerns[0],nkerns[1],4,4)
self.layer1 = LeNetConvPoolLayer(rng,
input=self.layer0.output,
image_shape=(batch_size, nkerns[0],
12, 12),
filter_shape=(nkerns[1], nkerns[0], 5,
5),
poolsize=(2, 2))
# the TanhLayer being fully-connected, it operates on 2D matrices of
# shape (batch_size,num_pixels) (i.e matrix of rasterized images).
# This will generate a matrix of shape (20,32*4*4) = (20,512)
self.layer2_input = self.layer1.output.flatten(2)
self.layer2 = HiddenLayer(rng,
input=self.layer2_input,
n_in=nkerns[1] * 4 * 4,
n_out=500,
activation=T.tanh)
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 = 500
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.layer2.output
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
