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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 OneHotCategorical distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
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 kullback_leibler
from tensorflow.python.ops.distributions import util as distribution_util
class OneHotCategorical(distribution.Distribution):
"""OneHotCategorical distribution.
The categorical distribution is parameterized by the log-probabilities
of a set of classes. The difference between OneHotCategorical and Categorical
distributions is that OneHotCategorical is a discrete distribution over
one-hot bit vectors whereas Categorical is a discrete distribution over
positive integers. OneHotCategorical is equivalent to Categorical except
Categorical has event_dim=() while OneHotCategorical has event_dim=K, where
K is the number of classes.
This class provides methods to create indexed batches of OneHotCategorical
distributions. If the provided `logits` or `probs` is rank 2 or higher, for
every fixed set of leading dimensions, the last dimension represents one
single OneHotCategorical distribution. When calling distribution
functions (e.g. `dist.prob(x)`), `logits` and `x` are broadcast to the
same shape (if possible). In all cases, the last dimension of `logits,x`
represents single OneHotCategorical distributions.
#### Examples
Creates a 3-class distribution, with the 2nd class, the most likely to be
drawn from.
```python
p = [0.1, 0.5, 0.4]
dist = OneHotCategorical(probs=p)
```
Creates a 3-class distribution, with the 2nd class the most likely to be
drawn from, using logits.
```python
logits = [-2, 2, 0]
dist = OneHotCategorical(logits=logits)
```
Creates a 3-class distribution, with the 3rd class is most likely to be drawn.
```python
# counts is a scalar.
p = [0.1, 0.4, 0.5]
dist = OneHotCategorical(probs=p)
dist.prob([0,1,0]) # Shape []
# p will be broadcast to [[0.1, 0.4, 0.5], [0.1, 0.4, 0.5]] to match.
samples = [[0,1,0], [1,0,0]]
dist.prob(samples) # Shape [2]
```
"""
def __init__(
self,
logits=None,
probs=None,
dtype=dtypes.int32,
validate_args=False,
allow_nan_stats=True,
name="OneHotCategorical"):
"""Initialize OneHotCategorical distributions using class log-probabilities.
Args:
logits: An N-D `Tensor`, `N >= 1`, representing the log probabilities of a
set of Categorical 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 Categorical 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]):
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(OneHotCategorical, self).__init__(
dtype=dtype,
reparameterization_type=distribution.NOT_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
graph_parents=[self._logits,
self._probs],
name=name)
@property
def event_size(self):
"""Scalar `int32` tensor: the number of classes."""
return self._event_size
@property
def logits(self):
"""Vector of coordinatewise logits."""
return self._logits
@property
def probs(self):
"""Vector of coordinatewise probabilities."""
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
if logits.get_shape().ndims == 2:
logits_2d = logits
else:
logits_2d = array_ops.reshape(logits, [-1, self.event_size])
samples = random_ops.multinomial(logits_2d, n, seed=seed)
samples = array_ops.transpose(samples)
samples = array_ops.one_hot(samples, self.event_size, dtype=self.dtype)
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, -1))
logits_2d = array_ops.reshape(logits, [-1, self.event_size])
x_2d = array_ops.reshape(x, [-1, self.event_size])
ret = -nn_ops.softmax_cross_entropy_with_logits(labels=x_2d,
logits=logits_2d)
# Reshape back to user-supplied batch and sample dims prior to 2D reshape.
ret = array_ops.reshape(ret, logits_shape)
return ret
def _entropy(self):
return -math_ops.reduce_sum(
nn_ops.log_softmax(self.logits) * self.probs, axis=-1)
def _mode(self):
ret = math_ops.argmax(self.logits, axis=self._batch_rank)
ret = array_ops.one_hot(ret, self.event_size, dtype=self.dtype)
ret.set_shape(self.logits.get_shape())
return ret
def _covariance(self):
p = self.probs
ret = -math_ops.matmul(p[..., None], p[..., None, :])
return array_ops.matrix_set_diag(ret, self._variance())
def _variance(self):
return self.probs * (1. - self.probs)
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)
@kullback_leibler.RegisterKL(OneHotCategorical, OneHotCategorical)
def _kl_categorical_categorical(a, b, name=None):
"""Calculate the batched KL divergence KL(a || b) with a, b OneHotCategorical.
Args:
a: instance of a OneHotCategorical distribution object.
b: instance of a OneHotCategorical distribution object.
name: (optional) Name to use for created operations.
default is "kl_categorical_categorical".
Returns:
Batchwise KL(a || b)
"""
with ops.name_scope(name, "kl_categorical_categorical", values=[
a.logits, b.logits]):
# sum(p ln(p / q))
return math_ops.reduce_sum(
nn_ops.softmax(a.logits) * (nn_ops.log_softmax(a.logits)
- nn_ops.log_softmax(b.logits)),
axis=-1)
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