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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""The RelaxedBernoulli distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.contrib.distributions.python.ops import distribution_util
from tensorflow.contrib.distributions.python.ops import logistic
from tensorflow.contrib.distributions.python.ops import transformed_distribution
# Bijectors must be directly imported because `remove_undocumented` prevents
# individual file imports.
from tensorflow.contrib.distributions.python.ops.bijectors.sigmoid import Sigmoid
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import check_ops
class RelaxedBernoulli(transformed_distribution.TransformedDistribution):
"""RelaxedBernoulli distribution with temperature and logits parameters.
The RelaxedBernoulli is a distribution over the unit interval (0,1), which
continuously approximates a Bernoulli. The degree of approximation is
controlled by a temperature: as the temperaturegoes to 0 the RelaxedBernoulli
becomes discrete with a distribution described by the `logits` or `probs`
parameters, as the temperature goes to infinity the RelaxedBernoulli
becomes the constant distribution that is identically 0.5.
The RelaxedBernoulli distribution is a reparameterized continuous
distribution that is the binary special case of the RelaxedOneHotCategorical
distribution (Maddison et al., 2016; Jang et al., 2016). For details on the
binary special case see the appendix of Maddison et al. (2016) where it is
referred to as BinConcrete. If you use this distribution, please cite both
papers.
Some care needs to be taken for loss functions that depend on the
log-probability of RelaxedBernoullis, because computing log-probabilities of
the RelaxedBernoulli can suffer from underflow issues. In many case loss
functions such as these are invariant under invertible transformations of
the random variables. The KL divergence, found in the variational autoencoder
loss, is an example. Because RelaxedBernoullis are sampled by by a Logistic
random variable followed by a `tf.sigmoid` op, one solution is to treat
the Logistic as the random variable and `tf.sigmoid` as downstream. The
KL divergences of two Logistics, which are always followed by a `tf.sigmoid`
op, is equivalent to evaluating KL divergences of RelaxedBernoulli samples.
See Maddison et al., 2016 for more details where this distribution is called
the BinConcrete.
An alternative approach is to evaluate Bernoulli log probability or KL
directly on relaxed samples, as done in Jang et al., 2016. In this case,
guarantees on the loss are usually violated. For instance, using a Bernoulli
KL in a relaxed ELBO is no longer a lower bound on the log marginal
probability of the observation. Thus care and early stopping are important.
#### Examples
Creates three continuous distributions, which approximate 3 Bernoullis with
probabilities (0.1, 0.5, 0.4). Samples from these distributions will be in
the unit interval (0,1).
```python
temperature = 0.5
p = [0.1, 0.5, 0.4]
dist = RelaxedBernoulli(temperature, probs=p)
```
Creates three continuous distributions, which approximate 3 Bernoullis with
logits (-2, 2, 0). Samples from these distributions will be in
the unit interval (0,1).
```python
temperature = 0.5
logits = [-2, 2, 0]
dist = RelaxedBernoulli(temperature, logits=logits)
```
Creates three continuous distributions, whose sigmoid approximate 3 Bernoullis
with logits (-2, 2, 0).
```python
temperature = 0.5
logits = [-2, 2, 0]
dist = Logistic(logits/temperature, 1./temperature)
samples = dist.sample()
sigmoid_samples = tf.sigmoid(samples)
# sigmoid_samples has the same distribution as samples from
# RelaxedBernoulli(temperature, logits=logits)
```
Creates three continuous distributions, which approximate 3 Bernoullis with
logits (-2, 2, 0). Samples from these distributions will be in
the unit interval (0,1). Because the temperature is very low, samples from
these distributions are almost discrete, usually taking values very close to 0
or 1.
```python
temperature = 1e-5
logits = [-2, 2, 0]
dist = RelaxedBernoulli(temperature, logits=logits)
```
Creates three continuous distributions, which approximate 3 Bernoullis with
logits (-2, 2, 0). Samples from these distributions will be in
the unit interval (0,1). Because the temperature is very high, samples from
these distributions are usually close to the (0.5, 0.5, 0.5) vector.
```python
temperature = 100
logits = [-2, 2, 0]
dist = RelaxedBernoulli(temperature, logits=logits)
```
Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution:
A Continuous Relaxation of Discrete Random Variables. 2016.
Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with
Gumbel-Softmax. 2016.
"""
def __init__(self,
temperature,
logits=None,
probs=None,
validate_args=False,
allow_nan_stats=True,
name="RelaxedBernoulli"):
"""Construct RelaxedBernoulli distributions.
Args:
temperature: An 0-D `Tensor`, representing the temperature
of a set of RelaxedBernoulli distributions. The temperature should be
positive.
logits: An N-D `Tensor` representing the log-odds
of a positive event. Each entry in the `Tensor` parametrizes
an independent RelaxedBernoulli distribution where the probability of an
event is sigmoid(logits). Only one of `logits` or `probs` should be
passed in.
probs: An N-D `Tensor` representing the probability of a positive event.
Each entry in the `Tensor` parameterizes an independent Bernoulli
distribution. Only one of `logits` or `probs` should be passed in.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may silently render incorrect
outputs.
allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
result is undefined. When `False`, an exception is raised if one or
more of the statistic's batch members are undefined.
name: Python `str` name prefixed to Ops created by this class.
Raises:
ValueError: If both `probs` and `logits` are passed, or if neither.
"""
parameters = locals()
with ops.name_scope(name, values=[logits, probs, temperature]):
with ops.control_dependencies([check_ops.assert_positive(temperature)]
if validate_args else []):
self._temperature = array_ops.identity(temperature, name="temperature")
self._logits, self._probs = distribution_util.get_logits_and_probs(
logits=logits, probs=probs, validate_args=validate_args)
super(RelaxedBernoulli, self).__init__(
distribution=logistic.Logistic(self._logits / self._temperature,
1. / self._temperature,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name + "/Logistic"),
bijector=Sigmoid(validate_args=validate_args),
validate_args=validate_args,
name=name)
self._parameters = parameters
@staticmethod
def _param_shapes(sample_shape):
return {"logits": ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)}
@property
def temperature(self):
"""Distribution parameter for the location."""
return self._temperature
@property
def logits(self):
"""Log-odds of `1`."""
return self._logits
@property
def probs(self):
"""Probability of `1`."""
return self._probs
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