def mlp(learning_rate=0.01, L1_reg=0.00, L2_reg=0.0001, n_epochs=1000,
batch_size=20, n_hidden=500):
"""
Stochastic gradient descent optimization for a multilayer perceptron
:type learning_rate: float
:param learning_rate: learning rate used (factor for stochatic gradient)
:type L1_reg: float
:param L1_reg: L1-norm's weight when added to the cost
:type L2_reg: float
:param L2_reg: L2-norm's weight when added to the cost
:type n_epochs: int
:param n_epochs: maximal number of epichs to run the optimizer
:param batch_size: size of bach processed
:param n_hidden: number of hidden outputs
"""
datasets = load_data(5000)
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] // batch_size
n_valid_batches = valid_set_x.get_value(borrow=True).shape[0] // batch_size
n_test_batches = test_set_x.get_value(borrow=True).shape[0] // batch_size
######################
# BUILD ACTUAL MODEL #
######################
print('... building the model ...')
# 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') # labels as 1D vector of [int] labels
rng = np.random.RandomState(13032016)
# construct the MLP class
classifier = MLP(
rng=rng,
input=x,
n_in=prep.SIZE[0] * prep.SIZE[1] * 3,
n_hidden=n_hidden,
n_out=3
)
# start-snippet-4
# the cost we minimize during training is the negative log liklihood of
# the model plus the regularization terms (L1 and L2)
cost = (
classifier.negative_log_likelihood(y)
+ L1_reg * classifier.L1
+ L2_reg * classifier.L2_sqr
)
# end-snippet-4
# 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: 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(
inputs=[index],
outputs=classifier.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]
}
)
# start-snippet-5
# compute the gradient of cost with respect to theta (stored in params)
# the resulting gradients will be stored in a list gparams
gparams = [T.grad(cost, param) for param in classifier.params]
# specify how to update the parameters of the model as a list of
# (variable, update expression_ pairs
updates = [
(param, param - learning_rate * gparam)
for param, gparam in zip(classifier.params, gparams)
]
# compiling a Theano function 'train model' that returns the cost, but
# at 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: train_set_x[index * batch_size: (index + 1) * batch_size],
y: train_set_y[index * batch_size: (index + 1) * batch_size]
}
)
# end-snippet-5
###############
# TRAIN MODEL #
###############
print('... training ...')
# early-stopping parameters
patience = 10000
patience_increase = 2 # wait this long when a new best is found
improvement_threshold = 0.995 # relative improvement considered significant
validation_frequency = min(n_train_batches, patience // 2)
# go thorugh this many minibatches before
# checking the network on the validation set;
# in this case we check every epoch
best_validation_loss = np.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 minibatch_index in range(n_train_batches):
minibatch_avg_cost = train_model(minibatch_index)
# iteration number
iter = (epoch - 1) * n_train_batches + minibatch_index
if (iter + 1) % validation_frequency == 0:
# computer zero-one loss on validation set
validation_losses = [validate_model(i) for i
in range(n_valid_batches)]
this_validation_loss = np.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 get 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)
best_validation_loss = this_validation_loss
best_iter = iter
# test it on on the test set
test_losses = [test_model(i) for i
in range(n_test_batches)]
test_score = np.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_mlp_model.pkl', 'wb') as f:
pickle.dump(classifier, f)
if patience <= iter:
done_looping = True
break
end_time = timeit.default_timer()
print(('Optimization complete. 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' % ((end_time - start_time) / 60.)), file=sys.stderr)
def evaluate_lenet5(learning_rate=0.1, n_epochs=200,
nkerns=[20, 50], batch_size=500):
"""
:type learning_rate: float
:param learning_rate: factor for stochastic gradient
:type n_epochs: int
:param n_epochs: maximal number of epochs to run the optimizer
:type nkerns: list of ints
:param nkerns: number of kernels on each layer
:param batch_size: size of batch
"""
rng = np.random.RandomState(20160313)
datasets = load_data(3500)
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')
# Reshape matrix of rasterized images of shape (batch_size, image w*h)
# to a 4D tensor, compatible with our LeNetConvPoolLayer
layer0_input = x.reshape((batch_size, 1, prep.SIZE[0], prep.SIZE[1]))
# Construct the first convolutional pooling layer:
# filtering reduces the image size to (size-5+1 , size-5+1) = (24, 24)
# maxpooling reduces this by factor of 1/2
# 4D output tensor is thus of shape (batch_size, nkerns[0], 12, 12)
layer0 = LeNetConvPoolLayer(
rng,
input=layer0_input,
image_shape=(batch_size, 1, prep.SIZE[0], prep.SIZE[1]),
filter_shape=(nkerns[0], 1, 5, 5),
poolsize=(2, 2)
)
new_size = ((prep.SIZE[0] - 5 + 1) // 2, (prep.SIZE[1] - 5 + 1 // 2))
# Construct the second convolutional pooling layer
# filtering reduces the image size as previous
layer1 = LeNetConvPoolLayer(
rng,
input=layer0.output,
image_shape=(batch_size, nkerns[0], new_size[0], new_size[1]),
filter_shape=(nkerns[1], nkerns[0], 5, 5),
poolsize=(2, 2)
)
new_size = ((new_size[0] -5 + 1) // 2, (new_size[1] -5 + 1 // 2))
# 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] * new_size),
# or (500, 50 * new_size[0] * new_size[1]) = (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] * new_size[0] * new_size[1],
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=3)
# 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 = [
(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 = np.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 = epoch + 1
for minibatch_index in range(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 range(n_valid_batches)]
this_validation_loss = np.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 range(n_test_batches)
]
test_score = np.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_mlp_model.pkl', 'wb') as f:
# pickle.dump(classifier, f)
if patience <= iter:
done_looping = True
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(('The code for file ' +
os.path.split(__file__)[1] +
' ran for %.2fm' % ((end_time - start_time) / 60.)), file=sys.stderr)