class SdA(object):
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]):
self.sigmoid_layers = []
self.dA_layers = []
self.params = []
self.n_layers = len(hidden_layers_sizes)
assert self.n_layers > 0
if not theano_rng:
theano_rng = RandomStreams(numpy_rng.randint(2 ** 30))
# allocate symbolic variables for the data
self.x = T.matrix('x') # the data is presented as rasterized images
self.y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
# The SdA is an MLP, for which all weights of intermediate layers
# are shared with a different denoising autoencoders
# We will first construct the SdA as a deep multilayer perceptron,
# and when constructing each sigmoidal layer we also construct a
# denoising autoencoder that shares weights with that layer
# During pretraining we will train these autoencoders (which will
# lead to chainging the weights of the MLP as well)
# During finetunining we will finish training the SdA by doing
# stochastich gradient descent on the MLP
for i in xrange(self.n_layers):
# construct the sigmoidal layer
# the size of the input is either the number of hidden units of
# the layer below or the input size if we are on the first layer
if i == 0:
input_size = n_ins
else:
input_size = hidden_layers_sizes[i - 1]
# the input to this layer is either the activation of the hidden
# layer below or the input of the SdA if you are on the first
# layer
if i == 0:
layer_input = self.x
else:
layer_input = self.sigmoid_layers[-1].output
sigmoid_layer = HiddenLayer(rng=numpy_rng,
input=layer_input,
n_in=input_size,
n_out=hidden_layers_sizes[i],
activation=T.nnet.sigmoid)
# add the layer to our list of layers
self.sigmoid_layers.append(sigmoid_layer)
# its arguably a philosophical question...
# but we are going to only declare that the parameters of the
# sigmoid_layers are parameters of the StackedDAA
# the visible biases in the dA are parameters of those
# dA, but not the SdA
self.params.extend(sigmoid_layer.params)
# Construct a denoising autoencoder that shared weights with this
# layer
dA_layer = dA(numpy_rng=numpy_rng,
theano_rng=theano_rng,
input=layer_input,
n_visible=input_size,
n_hidden=hidden_layers_sizes[i],
W=sigmoid_layer.W,
bhid=sigmoid_layer.b)
self.dA_layers.append(dA_layer)
# We now need to add a logistic layer on top of the MLP
self.logLayer = LogisticRegression(
input=self.sigmoid_layers[-1].output,
n_in=hidden_layers_sizes[-1], n_out=n_outs)
self.params.extend(self.logLayer.params)
# construct a function that implements one step of finetunining
# compute the cost for second phase of training,
# defined as the negative log likelihood
self.finetune_cost = self.logLayer.negative_log_likelihood(self.y)
# compute the gradients with respect to the model parameters
# symbolic variable that points to the number of errors made on the
# minibatch given by self.x and self.y
self.errors = self.logLayer.errors(self.y)
def pretraining_functions(self, train_set_x, batch_size):
''' Generates a list of functions, each of them implementing one
step in trainnig the dA corresponding to the layer with same index.
The function will require as input the minibatch index, and to train
a dA you just need to iterate, calling the corresponding function on
all minibatch indexes.
:type train_set_x: theano.tensor.TensorType
:param train_set_x: Shared variable that contains all datapoints used
for training the dA
:type batch_size: int
:param batch_size: size of a [mini]batch
:type learning_rate: float
:param learning_rate: learning rate used during training for any of
the dA layers
'''
# index to a [mini]batch
index = T.lscalar('index') # index to a minibatch
corruption_level = T.scalar('corruption') # % of corruption to use
learning_rate = T.scalar('lr') # learning rate to use
# number of batches
n_batches = train_set_x.get_value(borrow=True).shape[0] / batch_size
# begining of a batch, given `index`
batch_begin = index * batch_size
# ending of a batch given `index`
batch_end = batch_begin + batch_size
pretrain_fns = []
for dA in self.dA_layers:
# get the cost and the updates list
cost, updates = dA.get_cost_updates(corruption_level,
learning_rate)
# compile the theano function
fn = theano.function(inputs=[index,
theano.Param(corruption_level, default=0.2),
theano.Param(learning_rate, default=0.1)],
outputs=cost,
updates=updates,
givens={self.x: train_set_x[batch_begin:
batch_end]})
# append `fn` to the list of functions
pretrain_fns.append(fn)
return pretrain_fns
def build_finetune_functions(self, datasets, batch_size, learning_rate):
'''Generates a function `train` that implements one step of
finetuning, a function `validate` that computes the error on
a batch from the validation set, and a function `test` that
computes the error on a batch from the testing set
:type datasets: list of pairs of theano.tensor.TensorType
:param datasets: It is a list that contain all the datasets;
the has to contain three pairs, `train`,
`valid`, `test` in this order, where each pair
is formed of two Theano variables, one for the
datapoints, the other for the labels
:type batch_size: int
:param batch_size: size of a minibatch
:type learning_rate: float
:param learning_rate: learning rate used during finetune stage
'''
(train_set_x, train_set_y) = datasets[0]
(valid_set_x, valid_set_y) = datasets[1]
(test_set_x, test_set_y) = datasets[2]
# compute number of minibatches for training, validation and testing
n_valid_batches = valid_set_x.get_value(borrow=True).shape[0]
n_valid_batches /= batch_size
n_test_batches = test_set_x.get_value(borrow=True).shape[0]
n_test_batches /= batch_size
index = T.lscalar('index') # index to a [mini]batch
# compute the gradients with respect to the model parameters
gparams = T.grad(self.finetune_cost, self.params)
# compute list of fine-tuning updates
updates = {}
for param, gparam in zip(self.params, gparams):
updates[param] = param - gparam * learning_rate
train_fn = theano.function(inputs=[index],
outputs=self.finetune_cost,
updates=updates,
givens={
self.x: train_set_x[index * batch_size:
(index + 1) * batch_size],
self.y: train_set_y[index * batch_size:
(index + 1) * batch_size]})
test_score_i = theano.function([index], self.errors,
givens={
self.x: test_set_x[index * batch_size:
(index + 1) * batch_size],
self.y: test_set_y[index * batch_size:
(index + 1) * batch_size]})
valid_score_i = theano.function([index], self.errors,
givens={
self.x: valid_set_x[index * batch_size:
(index + 1) * batch_size],
self.y: valid_set_y[index * batch_size:
(index + 1) * batch_size]})
# Create a function that scans the entire validation set
def valid_score():
return [valid_score_i(i) for i in xrange(n_valid_batches)]
# Create a function that scans the entire test set
def test_score():
return [test_score_i(i) for i in xrange(n_test_batches)]
return train_fn, valid_score, test_score
def __init__(self, numpy_rng, theano_rng=None, n_ins=784,
hidden_layers_sizes=[500, 500], n_outs=10,
corruption_levels=[0.1, 0.1]):
self.sigmoid_layers = []
self.dA_layers = []
self.params = []
self.n_layers = len(hidden_layers_sizes)
assert self.n_layers > 0
if not theano_rng:
theano_rng = RandomStreams(numpy_rng.randint(2 ** 30))
# allocate symbolic variables for the data
self.x = T.matrix('x') # the data is presented as rasterized images
self.y = T.ivector('y') # the labels are presented as 1D vector of
# [int] labels
# The SdA is an MLP, for which all weights of intermediate layers
# are shared with a different denoising autoencoders
# We will first construct the SdA as a deep multilayer perceptron,
# and when constructing each sigmoidal layer we also construct a
# denoising autoencoder that shares weights with that layer
# During pretraining we will train these autoencoders (which will
# lead to chainging the weights of the MLP as well)
# During finetunining we will finish training the SdA by doing
# stochastich gradient descent on the MLP
for i in xrange(self.n_layers):
# construct the sigmoidal layer
# the size of the input is either the number of hidden units of
# the layer below or the input size if we are on the first layer
if i == 0:
input_size = n_ins
else:
input_size = hidden_layers_sizes[i - 1]
# the input to this layer is either the activation of the hidden
# layer below or the input of the SdA if you are on the first
# layer
if i == 0:
layer_input = self.x
else:
layer_input = self.sigmoid_layers[-1].output
sigmoid_layer = HiddenLayer(rng=numpy_rng,
input=layer_input,
n_in=input_size,
n_out=hidden_layers_sizes[i],
activation=T.nnet.sigmoid)
# add the layer to our list of layers
self.sigmoid_layers.append(sigmoid_layer)
# its arguably a philosophical question...
# but we are going to only declare that the parameters of the
# sigmoid_layers are parameters of the StackedDAA
# the visible biases in the dA are parameters of those
# dA, but not the SdA
self.params.extend(sigmoid_layer.params)
# Construct a denoising autoencoder that shared weights with this
# layer
dA_layer = dA(numpy_rng=numpy_rng,
theano_rng=theano_rng,
input=layer_input,
n_visible=input_size,
n_hidden=hidden_layers_sizes[i],
W=sigmoid_layer.W,
bhid=sigmoid_layer.b)
self.dA_layers.append(dA_layer)
# We now need to add a logistic layer on top of the MLP
self.logLayer = LogisticRegression(
input=self.sigmoid_layers[-1].output,
n_in=hidden_layers_sizes[-1], n_out=n_outs)
self.params.extend(self.logLayer.params)
# construct a function that implements one step of finetunining
# compute the cost for second phase of training,
# defined as the negative log likelihood
self.finetune_cost = self.logLayer.negative_log_likelihood(self.y)
# compute the gradients with respect to the model parameters
# symbolic variable that points to the number of errors made on the
# minibatch given by self.x and self.y
self.errors = self.logLayer.errors(self.y)
def evaluate_lenet5(learning_rate=0.15, n_epochs=500,
nkerns=[10, 20], batch_size=1):
rng = numpy.random.RandomState(23455)
datasets = load_data()
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 = (IMAGE_WIDTH, IMAGE_HEIGHT)
######################
# BUILD ACTUAL MODEL #
######################
print '... building the model'
layer0_input = x.reshape((batch_size, 1, IMAGE_WIDTH, IMAGE_HEIGHT))
# 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, IMAGE_WIDTH, IMAGE_HEIGHT),
filter_shape=(nkerns[0], 1, 5, 5), poolsize=(2, 2))
# due to filter + pool
new_width = (IMAGE_WIDTH - 5 + 1) / 2
new_height = (IMAGE_HEIGHT - 5 + 1) / 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], new_width, new_height),
filter_shape=(nkerns[1], nkerns[0], 5, 5), poolsize=(2, 2))
new_width = (new_width - 5 + 1) / 2
new_height = (new_height - 5 + 1) / 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] * new_width * new_height, 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=N_CLASSES)
# 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 dictionary by automatically looping over all
# (params[i],grads[i]) pairs.
updates = {}
for param_i, grad_i in zip(params, grads):
updates[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 = 1# 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 = 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 * 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("RECORD BROKEN")
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, test_score * 100.))
print >> sys.stderr, ('The code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.))
