def __init__(self, dimensions, noise=0.1, reconstruction_penalty=1.0,
sparsity_penalty=1.0, embedding_penalty=1.0,
learning_rate=0.01, seed=None):
"""Initialize a stack of autoencoders with sparsity penalty
dimensions is a python sequence of the input, hidden and output
activation unit of the stacked architecture.
TODO: implement fine-tuning by applying SGD on the encoder using a
divergence measure on the pairwise similarities in input and output
space as object function to minimize. E.g.: (t-)SNE or Elastic
Embedding.
"""
assert len(dimensions) >= 2
self.rng = np.random.RandomState(seed)
self.noise_rng = RandomStreams(seed)
# build a stack of autoencoders for the requested dimensions
self.autoencoders = []
previous_output = T.matrix('ae_in')
for in_dim, out_dim in zip(dimensions[:-1], dimensions[1:]):
ae = Autoencoder(in_dim, out_dim, tied=True, noise=noise,
rng=self.rng, noise_rng=self.noise_rng)
ae.build(previous_output)
previous_output = ae.output
self.autoencoders.append(ae)
# chain the encoding parts as a feed forward network
self.encoder = NNet(self.autoencoders, errors.mse)
self.encoder.build(T.matrix('enc_in'), T.vector('enc_target'))
# compile the training functions
self.reconstruction_penalty = reconstruction_penalty
self.sparsity_penalty = sparsity_penalty
self.embedding_penalty = embedding_penalty
self.pre_trainers = []
for ae in self.autoencoders:
cost = self.get_ae_cost(ae)
pre_train = theano.function(
[self.autoencoders[0].input],
cost,
updates=get_updates(ae.pre_params, cost, learning_rate)
)
self.pre_trainers.append(pre_train)
# compile the enconding function
self.encode = theano.function([self.encoder.input], self.encoder.output)
class SDAEmbedder(object):
"""Build a stack of denoising autoencoders to perform low dim embedding"""
def __init__(self, dimensions, noise=0.1, reconstruction_penalty=1.0,
sparsity_penalty=1.0, embedding_penalty=1.0,
learning_rate=0.01, seed=None):
"""Initialize a stack of autoencoders with sparsity penalty
dimensions is a python sequence of the input, hidden and output
activation unit of the stacked architecture.
TODO: implement fine-tuning by applying SGD on the encoder using a
divergence measure on the pairwise similarities in input and output
space as object function to minimize. E.g.: (t-)SNE or Elastic
Embedding.
"""
assert len(dimensions) >= 2
self.rng = np.random.RandomState(seed)
self.noise_rng = RandomStreams(seed)
# build a stack of autoencoders for the requested dimensions
self.autoencoders = []
previous_output = T.matrix('ae_in')
for in_dim, out_dim in zip(dimensions[:-1], dimensions[1:]):
ae = Autoencoder(in_dim, out_dim, tied=True, noise=noise,
rng=self.rng, noise_rng=self.noise_rng)
ae.build(previous_output)
previous_output = ae.output
self.autoencoders.append(ae)
# chain the encoding parts as a feed forward network
self.encoder = NNet(self.autoencoders, errors.mse)
self.encoder.build(T.matrix('enc_in'), T.vector('enc_target'))
# compile the training functions
self.reconstruction_penalty = reconstruction_penalty
self.sparsity_penalty = sparsity_penalty
self.embedding_penalty = embedding_penalty
self.pre_trainers = []
for ae in self.autoencoders:
cost = self.get_ae_cost(ae)
pre_train = theano.function(
[self.autoencoders[0].input],
cost,
updates=get_updates(ae.pre_params, cost, learning_rate)
)
self.pre_trainers.append(pre_train)
# compile the enconding function
self.encode = theano.function([self.encoder.input], self.encoder.output)
def pre_train(self, data, slice_=slice(None, None), batch_size=50,
epochs=100, checkpoint=10, patience=20, tolerance=1e-5):
"""Iteratively apply SGD to each autoencoder
If slice_ is provided, only the matching layers are trained (by default
all layers are trained).
"""
data = np.atleast_2d(data)
data = np.asanyarray(data, dtype=theano.config.floatX)
n_samples, n_features = data.shape
best_error = None
best_epoch = 0
n_batches = n_samples / batch_size
# select the trainers to use
trainers = self.pre_trainers[slice_]
shuffled = data.copy()
for i, trainer in enumerate(trainers):
for e in xrange(epochs):
# reshuffling data to enforce I.I.D. assumption
self.rng.shuffle(shuffled)
err = np.zeros(n_batches)
for b in xrange(n_batches):
batch_input = shuffled[b * batch_size:(b + 1) * batch_size]
err[b] = trainer(batch_input).mean()
error = err.mean()
if e % checkpoint == 0:
print "layer [%d/%d], epoch [%03d/%03d]: err: %0.5f" % (
i + 1, len(trainers), e + 1, epochs,
error)
if best_error is None or error < best_error - tolerance:
best_error = error
best_epoch = e
else:
if e - best_epoch > patience:
print "layer [%d/%d]: early stopping at epoch %d" % (
i + 1, len(trainers), e + 1)
break
def fine_tune(self, data, batch_size=50, epochs=100, learning_rate=0.1,
checkpoint=10, patience=20, tolerance=1e-5):
"""Use SGD to optimize the embedding computed by the encoder stack"""
data = np.atleast_2d(data)
data = np.asanyarray(data, dtype=theano.config.floatX)
n_samples, n_features = data.shape
best_error = None
best_epoch = 0
n_batches = n_samples / batch_size
cost = self.get_embedding_cost(self.autoencoders[-1])
tuner = theano.function(
[self.autoencoders[0].input],
cost,
updates=get_updates(self.encoder.params, cost, learning_rate)
)
shuffled = data.copy()
for e in xrange(epochs):
# reshuffling data to enforce I.I.D. assumption
self.rng.shuffle(shuffled)
err = np.zeros(n_batches)
for b in xrange(n_batches):
batch_input = shuffled[b * batch_size:(b + 1) * batch_size]
err[b] = tuner(batch_input).mean()
error = err.mean()
if e % checkpoint == 0:
print "fine tune: epoch [%03d/%03d]: err: %0.5f" % (
e + 1, epochs, error)
if best_error is None or error < best_error - tolerance:
best_error = error
best_epoch = e
else:
if e - best_epoch > patience:
print "fine tune: early stopping at epoch %d" % (e + 1)
break
def get_ae_cost(self, ae):
cost = 0.0
if self.reconstruction_penalty > 0:
cost += self.reconstruction_penalty * ae.cost
if self.sparsity_penalty > 0:
# assuming the activation of each unit lies in [-1, 1], take the
# L1 norm of the activation
# TODO: run a component wise online estimate of the activations
# using a exponential decay instead of the spatial sparsity
# constraint
cost += self.sparsity_penalty * T.mean(abs(ae.output + 1))
if self.embedding_penalty > 0:
cost += self.embedding_penalty * self.get_embedding_cost(ae)
return cost
def get_embedding_cost(self, ae, lambda_=0.5):
"""Local divergence from pairwise similarities in input and output
The following is derived from the Elastic Embedding cost from
M. Carreira-Perpinan 2010.
"""
ae_in = self.autoencoders[0]
# TODO: make it possible to provide dx2 and dx2.mean() in advance and
# online estimate dy2.mean() on the whole collection using a exponential
# decay
dx2 = T.sum((ae_in.input[:-1] - ae_in.input[1:]) ** 2, axis=1)
dy2 = T.sum((ae.output[:-1] - ae.output[1:]) ** 2, axis=1)
return (1 - lambda_) * T.mean(dy2 / dy2.mean() * T.exp(-dx2 / dx2.mean())) + \
lambda_ * T.mean(dx2 / dx2.mean() * T.exp(-dy2 / dy2.mean()))
