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relaxed_onehot_categorical.py
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relaxed_onehot_categorical.py
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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.
# ==============================================================================
"""Relaxed OneHotCategorical distribution classes."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.contrib.distributions.python.ops import bijectors
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
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops import random_ops
from tensorflow.python.ops.distributions import distribution
from tensorflow.python.ops.distributions import transformed_distribution
from tensorflow.python.ops.distributions import util as distribution_util
class ExpRelaxedOneHotCategorical(distribution.Distribution):
"""ExpRelaxedOneHotCategorical distribution with temperature and logits.
An ExpRelaxedOneHotCategorical distribution is a log-transformed
RelaxedOneHotCategorical distribution. The RelaxedOneHotCategorical is a
distribution over random probability vectors, vectors of positive real
values that sum to one, which continuously approximates a OneHotCategorical.
The degree of approximation is controlled by a temperature: as the temperature
goes to 0 the RelaxedOneHotCategorical becomes discrete with a distribution
described by the logits, as the temperature goes to infinity the
RelaxedOneHotCategorical becomes the constant distribution that is identically
the constant vector of (1/event_size, ..., 1/event_size).
Because computing log-probabilities of the RelaxedOneHotCategorical can
suffer from underflow issues, this class is one solution for loss
functions that depend on log-probabilities, such as the KL Divergence found
in the variational autoencoder loss. The KL divergence between two
distributions is invariant under invertible transformations, so evaluating
KL divergences of ExpRelaxedOneHotCategorical samples, which are always
followed by a `tf.exp` op, is equivalent to evaluating KL divergences of
RelaxedOneHotCategorical samples. See the appendix of Maddison et al., 2016
for more mathematical details, where this distribution is called the
ExpConcrete.
#### Examples
Creates a continuous distribution, whose exp approximates a 3-class one-hot
categorical distribution. The 2nd class is the most likely to be the
largest component in samples drawn from this distribution. If those samples
are followed by a `tf.exp` op, then they are distributed as a relaxed onehot
categorical.
```python
temperature = 0.5
p = [0.1, 0.5, 0.4]
dist = ExpRelaxedOneHotCategorical(temperature, probs=p)
samples = dist.sample()
exp_samples = tf.exp(samples)
# exp_samples has the same distribution as samples from
# RelaxedOneHotCategorical(temperature, probs=p)
```
Creates a continuous distribution, whose exp approximates a 3-class one-hot
categorical distribution. The 2nd class is the most likely to be the
largest component in samples drawn from this distribution.
```python
temperature = 0.5
logits = [-2, 2, 0]
dist = ExpRelaxedOneHotCategorical(temperature, logits=logits)
samples = dist.sample()
exp_samples = tf.exp(samples)
# exp_samples has the same distribution as samples from
# RelaxedOneHotCategorical(temperature, probs=p)
```
Creates a continuous distribution, whose exp approximates a 3-class one-hot
categorical distribution. Because the temperature is very low, samples from
this distribution are almost discrete, with one component almost 0 and the
others very negative. The 2nd class is the most likely to be the largest
component in samples drawn from this distribution.
```python
temperature = 1e-5
logits = [-2, 2, 0]
dist = ExpRelaxedOneHotCategorical(temperature, logits=logits)
samples = dist.sample()
exp_samples = tf.exp(samples)
# exp_samples has the same distribution as samples from
# RelaxedOneHotCategorical(temperature, probs=p)
```
Creates a continuous distribution, whose exp approximates a 3-class one-hot
categorical distribution. Because the temperature is very high, samples from
this distribution are usually close to the (-log(3), -log(3), -log(3)) vector.
The 2nd class is still the most likely to be the largest component
in samples drawn from this distribution.
```python
temperature = 10
logits = [-2, 2, 0]
dist = ExpRelaxedOneHotCategorical(temperature, logits=logits)
samples = dist.sample()
exp_samples = tf.exp(samples)
# exp_samples has the same distribution as samples from
# RelaxedOneHotCategorical(temperature, probs=p)
```
Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution:
A Continuous Relaxation of Discrete Random Variables. 2016.
"""
def __init__(
self,
temperature,
logits=None,
probs=None,
dtype=dtypes.float32,
validate_args=False,
allow_nan_stats=True,
name="ExpRelaxedOneHotCategorical"):
"""Initialize ExpRelaxedOneHotCategorical using class log-probabilities.
Args:
temperature: An 0-D `Tensor`, representing the temperature
of a set of ExpRelaxedCategorical distributions. The temperature should
be positive.
logits: An N-D `Tensor`, `N >= 1`, representing the log probabilities
of a set of ExpRelaxedCategorical distributions. The first
`N - 1` dimensions index into a batch of independent distributions and
the last dimension represents a vector of logits for each class. Only
one of `logits` or `probs` should be passed in.
probs: An N-D `Tensor`, `N >= 1`, representing the probabilities
of a set of ExpRelaxedCategorical distributions. The first
`N - 1` dimensions index into a batch of independent distributions and
the last dimension represents a vector of probabilities for each
class. Only one of `logits` or `probs` should be passed in.
dtype: The type of the event samples (default: int32).
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.
"""
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._temperature_2d = array_ops.reshape(temperature, [-1, 1],
name="temperature_2d")
self._logits, self._probs = distribution_util.get_logits_and_probs(
name=name, logits=logits, probs=probs, validate_args=validate_args,
multidimensional=True)
logits_shape_static = self._logits.get_shape().with_rank_at_least(1)
if logits_shape_static.ndims is not None:
self._batch_rank = ops.convert_to_tensor(
logits_shape_static.ndims - 1,
dtype=dtypes.int32,
name="batch_rank")
else:
with ops.name_scope(name="batch_rank"):
self._batch_rank = array_ops.rank(self._logits) - 1
with ops.name_scope(name="event_size"):
self._event_size = array_ops.shape(self._logits)[-1]
super(ExpRelaxedOneHotCategorical, self).__init__(
dtype=dtype,
reparameterization_type=distribution.FULLY_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=[self._logits,
self._probs,
self._temperature],
name=name)
@property
def event_size(self):
"""Scalar `int32` tensor: the number of classes."""
return self._event_size
@property
def temperature(self):
"""Batchwise temperature tensor of a RelaxedCategorical."""
return self._temperature
@property
def logits(self):
"""Vector of coordinatewise logits."""
return self._logits
@property
def probs(self):
"""Vector of probabilities summing to one."""
return self._probs
def _batch_shape_tensor(self):
return array_ops.shape(self._logits)[:-1]
def _batch_shape(self):
return self.logits.get_shape()[:-1]
def _event_shape_tensor(self):
return array_ops.shape(self.logits)[-1:]
def _event_shape(self):
return self.logits.get_shape().with_rank_at_least(1)[-1:]
def _sample_n(self, n, seed=None):
sample_shape = array_ops.concat([[n], array_ops.shape(self.logits)], 0)
logits = self.logits * array_ops.ones(sample_shape)
logits_2d = array_ops.reshape(logits, [-1, self.event_size])
# Uniform variates must be sampled from the open-interval `(0, 1)` rather
# than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
# because it is the smallest, positive, "normal" number. A "normal" number
# is such that the mantissa has an implicit leading 1. Normal, positive
# numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
# this case, a subnormal number (i.e., np.nextafter) can cause us to sample
# 0.
uniform = random_ops.random_uniform(
shape=array_ops.shape(logits_2d),
minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
maxval=1.,
dtype=self.dtype,
seed=seed)
gumbel = -math_ops.log(-math_ops.log(uniform))
noisy_logits = math_ops.div(gumbel + logits_2d, self._temperature_2d)
samples = nn_ops.log_softmax(noisy_logits)
ret = array_ops.reshape(samples, sample_shape)
return ret
def _log_prob(self, x):
x = self._assert_valid_sample(x)
# broadcast logits or x if need be.
logits = self.logits
if (not x.get_shape().is_fully_defined() or
not logits.get_shape().is_fully_defined() or
x.get_shape() != logits.get_shape()):
logits = array_ops.ones_like(x, dtype=logits.dtype) * logits
x = array_ops.ones_like(logits, dtype=x.dtype) * x
logits_shape = array_ops.shape(math_ops.reduce_sum(logits, axis=[-1]))
logits_2d = array_ops.reshape(logits, [-1, self.event_size])
x_2d = array_ops.reshape(x, [-1, self.event_size])
# compute the normalization constant
k = math_ops.cast(self.event_size, x.dtype)
log_norm_const = (math_ops.lgamma(k)
+ (k - 1.)
* math_ops.log(self.temperature))
# compute the unnormalized density
log_softmax = nn_ops.log_softmax(logits_2d - x_2d * self._temperature_2d)
log_unnorm_prob = math_ops.reduce_sum(log_softmax, [-1], keep_dims=False)
# combine unnormalized density with normalization constant
log_prob = log_norm_const + log_unnorm_prob
# Reshapes log_prob to be consistent with shape of user-supplied logits
ret = array_ops.reshape(log_prob, logits_shape)
return ret
def _prob(self, x):
return math_ops.exp(self._log_prob(x))
def _assert_valid_sample(self, x):
if not self.validate_args:
return x
return control_flow_ops.with_dependencies([
check_ops.assert_non_positive(x),
distribution_util.assert_close(
array_ops.zeros([], dtype=self.dtype),
math_ops.reduce_logsumexp(x, axis=[-1])),
], x)
class RelaxedOneHotCategorical(
transformed_distribution.TransformedDistribution):
"""RelaxedOneHotCategorical distribution with temperature and logits.
The RelaxedOneHotCategorical is a distribution over random probability
vectors, vectors of positive real values that sum to one, which continuously
approximates a OneHotCategorical. The degree of approximation is controlled by
a temperature: as the temperaturegoes to 0 the RelaxedOneHotCategorical
becomes discrete with a distribution described by the `logits` or `probs`
parameters, as the temperature goes to infinity the RelaxedOneHotCategorical
becomes the constant distribution that is identically the constant vector of
(1/event_size, ..., 1/event_size).
The RelaxedOneHotCategorical distribution was concurrently introduced as the
Gumbel-Softmax (Jang et al., 2016) and Concrete (Maddison et al., 2016)
distributions for use as a reparameterized continuous approximation to the
`Categorical` one-hot distribution. If you use this distribution, please cite
both papers.
#### Examples
Creates a continuous distribution, which approximates a 3-class one-hot
categorical distribution. The 2nd class is the most likely to be the
largest component in samples drawn from this distribution.
```python
temperature = 0.5
p = [0.1, 0.5, 0.4]
dist = RelaxedOneHotCategorical(temperature, probs=p)
```
Creates a continuous distribution, which approximates a 3-class one-hot
categorical distribution. The 2nd class is the most likely to be the
largest component in samples drawn from this distribution.
```python
temperature = 0.5
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)
```
Creates a continuous distribution, which approximates a 3-class one-hot
categorical distribution. Because the temperature is very low, samples from
this distribution are almost discrete, with one component almost 1 and the
others nearly 0. The 2nd class is the most likely to be the largest component
in samples drawn from this distribution.
```python
temperature = 1e-5
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)
```
Creates a continuous distribution, which approximates a 3-class one-hot
categorical distribution. Because the temperature is very high, samples from
this distribution are usually close to the (1/3, 1/3, 1/3) vector. The 2nd
class is still the most likely to be the largest component
in samples drawn from this distribution.
```python
temperature = 10
logits = [-2, 2, 0]
dist = RelaxedOneHotCategorical(temperature, logits=logits)
```
Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with
Gumbel-Softmax. 2016.
Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution:
A Continuous Relaxation of Discrete Random Variables. 2016.
"""
def __init__(
self,
temperature,
logits=None,
probs=None,
dtype=dtypes.float32,
validate_args=False,
allow_nan_stats=True,
name="RelaxedOneHotCategorical"):
"""Initialize RelaxedOneHotCategorical using class log-probabilities.
Args:
temperature: An 0-D `Tensor`, representing the temperature
of a set of RelaxedOneHotCategorical distributions. The temperature
should be positive.
logits: An N-D `Tensor`, `N >= 1`, representing the log probabilities
of a set of RelaxedOneHotCategorical distributions. The first
`N - 1` dimensions index into a batch of independent distributions and
the last dimension represents a vector of logits for each class. Only
one of `logits` or `probs` should be passed in.
probs: An N-D `Tensor`, `N >= 1`, representing the probabilities
of a set of RelaxedOneHotCategorical distributions. The first `N - 1`
dimensions index into a batch of independent distributions and the last
dimension represents a vector of probabilities for each class. Only one
of `logits` or `probs` should be passed in.
dtype: The type of the event samples (default: int32).
validate_args: Unused in this distribution.
allow_nan_stats: Python `bool`, default `True`. If `False`, raise an
exception if a statistic (e.g. mean/mode/etc...) is undefined for any
batch member. If `True`, batch members with valid parameters leading to
undefined statistics will return NaN for this statistic.
name: A name for this distribution (optional).
"""
dist = ExpRelaxedOneHotCategorical(temperature,
logits=logits,
probs=probs,
dtype=dtype,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats)
super(RelaxedOneHotCategorical, self).__init__(dist,
bijectors.Exp(event_ndims=1),
name=name)