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finite_discrete.py
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finite_discrete.py
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# Copyright 2018 The TensorFlow Probability Authors.
#
# 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.
# ============================================================================
"""FiniteDiscrete distribution class."""
import numpy as np
import tensorflow.compat.v2 as tf
from tensorflow_probability.python.bijectors import ascending
from tensorflow_probability.python.bijectors import softmax_centered as softmax_centered_bijector
from tensorflow_probability.python.bijectors import softplus as softplus_bijector
from tensorflow_probability.python.distributions import categorical
from tensorflow_probability.python.distributions import distribution
from tensorflow_probability.python.internal import assert_util
from tensorflow_probability.python.internal import distribution_util as dist_util
from tensorflow_probability.python.internal import dtype_util
from tensorflow_probability.python.internal import parameter_properties
from tensorflow_probability.python.internal import prefer_static as ps
from tensorflow_probability.python.internal import reparameterization
from tensorflow_probability.python.internal import tensor_util
from tensorflow_probability.python.internal import tensorshape_util
__all__ = [
'FiniteDiscrete',
]
class FiniteDiscrete(
distribution.DiscreteDistributionMixin,
distribution.AutoCompositeTensorDistribution):
"""The finite discrete distribution.
The FiniteDiscrete distribution is parameterized by either probabilities or
log-probabilities of a set of `K` possible outcomes, which is defined by
a strictly ascending list of `K` values.
Note: log_prob, prob, cdf, mode, and entropy are differentiable with respect
to `logits` or `probs` but not with respect to `outcomes`.
#### Mathematical Details
The probability mass function (pmf) is,
```none
pmf(x; pi, qi) = prod_j pi_j**[x == qi_j]
```
#### Examples
```python
# Initialize a discrete distribution with 4 possible outcomes and the 2nd
# outcome being most likely.
dist = FiniteDiscrete([1., 2., 4., 8.], probs=[0.1, 0.4, 0.3, 0.2])
dist.prob(2.)
# ==> 0.4
# Using logits to initialize a discrete distribution with 4 possible outcomes
# and the 2nd outcome being most likely.
dist = FiniteDiscrete([1., 2., 4., 8.], logits=np.log([0.1, 0.4, 0.3, 0.2]))
dist.prob(2.)
# ==> 0.4
```
"""
def __init__(self,
outcomes,
logits=None,
probs=None,
rtol=None,
atol=None,
validate_args=False,
allow_nan_stats=True,
name='FiniteDiscrete'):
"""Construct a finite discrete contribution.
Args:
outcomes: A 1-D floating or integer `Tensor`, representing a list of
possible outcomes in strictly ascending order.
logits: A floating N-D `Tensor`, `N >= 1`, representing the log
probabilities of a set of FiniteDiscrete distributions. The first `N -
1` dimensions index into a batch of independent distributions and the
last dimension represents a vector of logits for each discrete value.
Only one of `logits` or `probs` should be passed in.
probs: A floating N-D `Tensor`, `N >= 1`, representing the probabilities
of a set of FiniteDiscrete distributions. The first `N - 1` dimensions
index into a batch of independent distributions and the last dimension
represents a vector of probabilities for each discrete value. Only one
of `logits` or `probs` should be passed in.
rtol: `Tensor` with same `dtype` as `outcomes`. The relative tolerance for
floating number comparison. Only effective when `outcomes` is a floating
`Tensor`. Default is `10 * eps`.
atol: `Tensor` with same `dtype` as `outcomes`. The absolute tolerance for
floating number comparison. Only effective when `outcomes` is a floating
`Tensor`. Default is `10 * eps`.
validate_args: Python `bool`, default `False`. When `True` distribution
parameters are checked for validity despite possibly degrading runtime
performance. When `False` invalid inputs may 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 = dict(locals())
with tf.name_scope(name) as name:
outcomes_dtype = dtype_util.common_dtype(
[outcomes], dtype_hint=tf.float32)
self._outcomes = tensor_util.convert_nonref_to_tensor(
outcomes, dtype_hint=outcomes_dtype, name='outcomes')
if dtype_util.is_floating(self._outcomes.dtype):
eps = np.finfo(dtype_util.as_numpy_dtype(outcomes_dtype)).eps
self._rtol = 10 * eps if rtol is None else rtol
self._atol = 10 * eps if atol is None else atol
else:
self._rtol = None
self._atol = None
self._categorical = categorical.Categorical(
logits=logits,
probs=probs,
dtype=tf.int32,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats)
super(FiniteDiscrete, self).__init__(
dtype=self._outcomes.dtype,
reparameterization_type=reparameterization.NOT_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
name=name)
@classmethod
def _parameter_properties(cls, dtype, num_classes=None):
# pylint: disable=g-long-lambda
return dict(
outcomes=parameter_properties.ParameterProperties(
event_ndims=None,
shape_fn=lambda sample_shape: [num_classes],
default_constraining_bijector_fn=ascending.Ascending()),
logits=parameter_properties.ParameterProperties(
event_ndims=1,
shape_fn=lambda sample_shape: ps.concat(
[sample_shape, [num_classes]], axis=0)),
probs=parameter_properties.ParameterProperties(
event_ndims=1,
shape_fn=lambda sample_shape: ps.concat(
[sample_shape, [num_classes]], axis=0),
default_constraining_bijector_fn=softmax_centered_bijector
.SoftmaxCentered,
is_preferred=False),
rtol=parameter_properties.ParameterProperties(
event_ndims=None, # TODO(b/187469130): standardize batch semantics.
default_constraining_bijector_fn=(
lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype))),
is_preferred=False),
atol=parameter_properties.ParameterProperties(
event_ndims=None, # TODO(b/187469130): standardize batch semantics.
default_constraining_bijector_fn=(
lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype))),
is_preferred=False))
# pylint: enable=g-long-lambda
@property
def outcomes(self):
return self._outcomes
@property
def logits(self):
"""Input argument `logits`."""
return self._categorical.logits
@property
def probs(self):
"""Input argument `probs`."""
return self._categorical.probs
def _event_shape_tensor(self):
return tf.constant([], dtype=tf.int32)
def _event_shape(self):
return tf.TensorShape([])
def _cdf(self, x):
x = tf.convert_to_tensor(x, name='x')
flat_x = tf.reshape(x, shape=[-1])
upper_bound = tf.searchsorted(self.outcomes, values=flat_x, side='right')
values_at_ub = tf.gather(
self.outcomes,
indices=tf.minimum(upper_bound, ps.shape(self.outcomes)[-1] - 1))
should_use_upper_bound = self._is_equal_or_close(flat_x, values_at_ub)
indices = tf.where(should_use_upper_bound, upper_bound, upper_bound - 1)
indices = tf.reshape(indices, shape=dist_util.prefer_static_shape(x))
indices_non_negative = tf.where(
tf.equal(indices, -1), tf.zeros([], indices.dtype), indices)
cdf = self._categorical.cdf(indices_non_negative)
return tf.where(tf.equal(indices, -1), tf.zeros([], cdf.dtype), cdf)
def _entropy(self):
return self._categorical.entropy()
def _is_equal_or_close(self, a, b):
if dtype_util.is_integer(self.outcomes.dtype):
return tf.equal(a, b)
return tf.abs(a - b) < self._atol + self._rtol * tf.abs(b)
def _log_prob(self, x):
x = tf.convert_to_tensor(x, name='x')
right_indices = tf.minimum(
tf.size(self.outcomes) - 1,
tf.reshape(
tf.searchsorted(
self.outcomes, values=tf.reshape(x, shape=[-1]), side='right'),
ps.shape(x)))
use_right_indices = self._is_equal_or_close(
x, tf.gather(self.outcomes, indices=right_indices))
left_indices = tf.maximum(0, right_indices - 1)
use_left_indices = self._is_equal_or_close(
x, tf.gather(self.outcomes, indices=left_indices))
log_probs = self._categorical.log_prob(
tf.where(use_left_indices, left_indices, right_indices))
return tf.where(
tf.logical_not(use_left_indices | use_right_indices),
dtype_util.as_numpy_dtype(log_probs.dtype)(-np.inf),
log_probs)
def _mean(self, probs=None):
if probs is None:
probs = self._categorical.probs_parameter()
outcomes = self.outcomes
if dtype_util.is_integer(outcomes.dtype):
if self._validate_args:
outcomes = dist_util.embed_check_integer_casting_closed(
outcomes, target_dtype=probs.dtype)
outcomes = tf.cast(outcomes, dtype=probs.dtype)
return tf.tensordot(outcomes, probs, axes=[[0], [-1]])
def _mode(self):
return tf.gather(self.outcomes, indices=self._categorical.mode())
def _sample_n(self, n, seed=None, **distribution_kwargs):
return tf.gather(
self.outcomes,
indices=self._categorical.sample(
sample_shape=[n], seed=seed, **distribution_kwargs))
def _variance(self):
probs = self._categorical.probs_parameter()
outcomes = tf.broadcast_to(self.outcomes, shape=ps.shape(probs))
if dtype_util.is_integer(outcomes.dtype):
if self._validate_args:
outcomes = dist_util.embed_check_integer_casting_closed(
outcomes, target_dtype=probs.dtype)
outcomes = tf.cast(outcomes, dtype=probs.dtype)
square_d = tf.math.squared_difference(
outcomes, self._mean(probs)[..., tf.newaxis])
return tf.reduce_sum(probs * square_d, axis=-1)
def logits_parameter(self, name=None):
"""Logits vec computed from non-`None` input arg (`probs` or `logits`)."""
with self._name_and_control_scope(name or 'logits_parameter'):
return self._categorical.logits_parameter()
def probs_parameter(self, name=None):
"""Probs vec computed from non-`None` input arg (`probs` or `logits`)."""
with self._name_and_control_scope(name or 'probs_parameter'):
return self._categorical.probs_parameter()
def _default_event_space_bijector(self):
return
def _parameter_control_dependencies(self, is_init):
assertions = []
# For `logits` and `probs`, we only want to have an assertion on what the
# user actually passed. For now, we access the underlying categorical's
# _logits and _probs directly. After the 2019-10-01 deprecation, it would
# also work to use .logits() and .probs().
logits = self._categorical._logits
probs = self._categorical._probs
outcomes = self._outcomes
validate_args = self._validate_args
# Build all shape and dtype checks during the `is_init` call.
if is_init:
def validate_equal_last_dim(tensor_a, tensor_b, message):
event_size_a = tf.compat.dimension_value(tensor_a.shape[-1])
event_size_b = tf.compat.dimension_value(tensor_b.shape[-1])
if event_size_a is not None and event_size_b is not None:
if event_size_a != event_size_b:
raise ValueError(message)
elif validate_args:
return assert_util.assert_equal(
tf.shape(tensor_a)[-1], tf.shape(tensor_b)[-1], message=message)
message = 'Size of outcomes must be greater than 0.'
if tensorshape_util.num_elements(outcomes.shape) is not None:
if tensorshape_util.num_elements(outcomes.shape) == 0:
raise ValueError(message)
elif validate_args:
assertions.append(
tf.assert_greater(tf.size(outcomes), 0, message=message))
if logits is not None:
maybe_assert = validate_equal_last_dim(
outcomes,
# pylint: disable=protected-access
self._categorical._logits,
# pylint: enable=protected-access
message='Last dimension of outcomes and logits must be equal size.')
if maybe_assert:
assertions.append(maybe_assert)
if probs is not None:
maybe_assert = validate_equal_last_dim(
outcomes,
probs,
message='Last dimension of outcomes and probs must be equal size.')
if maybe_assert:
assertions.append(maybe_assert)
message = 'Rank of outcomes must be 1.'
ndims = tensorshape_util.rank(outcomes.shape)
if ndims is not None:
if ndims != 1:
raise ValueError(message)
elif validate_args:
assertions.append(assert_util.assert_rank(outcomes, 1, message=message))
if not validate_args:
assert not assertions # Should never happen.
return []
if is_init != tensor_util.is_ref(outcomes):
assertions.append(
assert_util.assert_equal(
tf.math.is_strictly_increasing(outcomes),
True,
message='outcomes is not strictly increasing.'))
return assertions