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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 Categorical distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_shape
from tensorflow.python.ops import array_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 Categorical(distribution.Distribution):
"""Categorical distribution.
The categorical distribution is parameterized by the log-probabilities
of a set of classes.
#### 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 = Categorical(probs=p)
```
Creates a 3-class distribution, with the 2nd class the most likely to be
drawn from, using logits.
```python
logits = [-50, 400, 40]
dist = Categorical(logits=logits)
```
Creates a 3-class distribution, with the 3rd class is most likely to be drawn.
The distribution functions can be evaluated on counts.
```python
# counts is a scalar.
p = [0.1, 0.4, 0.5]
dist = Categorical(probs=p)
dist.prob(0) # Shape []
# p will be broadcast to [[0.1, 0.4, 0.5], [0.1, 0.4, 0.5]] to match counts.
counts = [1, 0]
dist.prob(counts) # Shape [2]
# p will be broadcast to shape [3, 5, 7, 3] to match counts.
counts = [[...]] # Shape [5, 7, 3]
dist.prob(counts) # Shape [5, 7, 3]
```
"""
def __init__(
self,
logits=None,
probs=None,
dtype=dtypes.int32,
validate_args=False,
allow_nan_stats=True,
name="Categorical"):
"""Initialize Categorical 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(
logits=logits,
probs=probs,
validate_args=validate_args,
multidimensional=True,
name=name)
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
logits_shape = array_ops.shape(self._logits, name="logits_shape")
if logits_shape_static[-1].value is not None:
self._event_size = ops.convert_to_tensor(
logits_shape_static[-1].value,
dtype=dtypes.int32,
name="event_size")
else:
with ops.name_scope(name="event_size"):
self._event_size = logits_shape[self._batch_rank]
if logits_shape_static[:-1].is_fully_defined():
self._batch_shape_val = constant_op.constant(
logits_shape_static[:-1].as_list(),
dtype=dtypes.int32,
name="batch_shape")
else:
with ops.name_scope(name="batch_shape"):
self._batch_shape_val = logits_shape[:-1]
super(Categorical, 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.identity(self._batch_shape_val)
def _batch_shape(self):
return self.logits.get_shape()[:-1]
def _event_shape_tensor(self):
return constant_op.constant([], dtype=dtypes.int32)
def _event_shape(self):
return tensor_shape.scalar()
def _sample_n(self, n, seed=None):
if self.logits.get_shape().ndims == 2:
logits_2d = self.logits
else:
logits_2d = array_ops.reshape(self.logits, [-1, self.event_size])
samples = random_ops.multinomial(logits_2d, n, seed=seed)
samples = math_ops.cast(samples, self.dtype)
ret = array_ops.reshape(
array_ops.transpose(samples),
array_ops.concat([[n], self.batch_shape_tensor()], 0))
return ret
def _log_prob(self, k):
k = ops.convert_to_tensor(k, name="k")
if self.logits.get_shape()[:-1] == k.get_shape():
logits = self.logits
else:
logits = self.logits * array_ops.ones_like(
array_ops.expand_dims(k, -1), dtype=self.logits.dtype)
logits_shape = array_ops.shape(logits)[:-1]
k *= array_ops.ones(logits_shape, dtype=k.dtype)
k.set_shape(tensor_shape.TensorShape(logits.get_shape()[:-1]))
return -nn_ops.sparse_softmax_cross_entropy_with_logits(labels=k,
logits=logits)
def _prob(self, k):
return math_ops.exp(self._log_prob(k))
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, dimension=self._batch_rank)
ret = math_ops.cast(ret, self.dtype)
ret.set_shape(self.batch_shape)
return ret
@kullback_leibler.RegisterKL(Categorical, Categorical)
def _kl_categorical_categorical(a, b, name=None):
"""Calculate the batched KL divergence KL(a || b) with a and b Categorical.
Args:
a: instance of a Categorical distribution object.
b: instance of a Categorical 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(probs log(probs / (1 - probs)))
delta_log_probs1 = (nn_ops.log_softmax(a.logits) -
nn_ops.log_softmax(b.logits))
return math_ops.reduce_sum(nn_ops.softmax(a.logits) * delta_log_probs1,
axis=-1)
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