1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
|
# 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.
# ==============================================================================
"""Registration and usage mechanisms for KL-divergences."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.util import deprecation
from tensorflow.python.util import tf_inspect
from tensorflow.python.util.tf_export import tf_export
_DIVERGENCES = {}
__all__ = [
"RegisterKL",
"kl_divergence",
]
def _registered_kl(type_a, type_b):
"""Get the KL function registered for classes a and b."""
hierarchy_a = tf_inspect.getmro(type_a)
hierarchy_b = tf_inspect.getmro(type_b)
dist_to_children = None
kl_fn = None
for mro_to_a, parent_a in enumerate(hierarchy_a):
for mro_to_b, parent_b in enumerate(hierarchy_b):
candidate_dist = mro_to_a + mro_to_b
candidate_kl_fn = _DIVERGENCES.get((parent_a, parent_b), None)
if not kl_fn or (candidate_kl_fn and candidate_dist < dist_to_children):
dist_to_children = candidate_dist
kl_fn = candidate_kl_fn
return kl_fn
@deprecation.deprecated(
"2019-01-01",
"The TensorFlow Distributions library has moved to "
"TensorFlow Probability "
"(https://github.com/tensorflow/probability). You "
"should update all references to use `tfp.distributions` "
"instead of `tf.distributions`.",
warn_once=True)
@tf_export("distributions.kl_divergence")
def kl_divergence(distribution_a, distribution_b,
allow_nan_stats=True, name=None):
"""Get the KL-divergence KL(distribution_a || distribution_b).
If there is no KL method registered specifically for `type(distribution_a)`
and `type(distribution_b)`, then the class hierarchies of these types are
searched.
If one KL method is registered between any pairs of classes in these two
parent hierarchies, it is used.
If more than one such registered method exists, the method whose registered
classes have the shortest sum MRO paths to the input types is used.
If more than one such shortest path exists, the first method
identified in the search is used (favoring a shorter MRO distance to
`type(distribution_a)`).
Args:
distribution_a: The first distribution.
distribution_b: The second distribution.
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.
Returns:
A Tensor with the batchwise KL-divergence between `distribution_a`
and `distribution_b`.
Raises:
NotImplementedError: If no KL method is defined for distribution types
of `distribution_a` and `distribution_b`.
"""
kl_fn = _registered_kl(type(distribution_a), type(distribution_b))
if kl_fn is None:
raise NotImplementedError(
"No KL(distribution_a || distribution_b) registered for distribution_a "
"type %s and distribution_b type %s"
% (type(distribution_a).__name__, type(distribution_b).__name__))
with ops.name_scope("KullbackLeibler"):
kl_t = kl_fn(distribution_a, distribution_b, name=name)
if allow_nan_stats:
return kl_t
# Check KL for NaNs
kl_t = array_ops.identity(kl_t, name="kl")
with ops.control_dependencies([
control_flow_ops.Assert(
math_ops.logical_not(
math_ops.reduce_any(math_ops.is_nan(kl_t))),
["KL calculation between %s and %s returned NaN values "
"(and was called with allow_nan_stats=False). Values:"
% (distribution_a.name, distribution_b.name), kl_t])]):
return array_ops.identity(kl_t, name="checked_kl")
@deprecation.deprecated(
"2019-01-01",
"The TensorFlow Distributions library has moved to "
"TensorFlow Probability "
"(https://github.com/tensorflow/probability). You "
"should update all references to use `tfp.distributions` "
"instead of `tf.distributions`.",
warn_once=True)
def cross_entropy(ref, other,
allow_nan_stats=True, name=None):
"""Computes the (Shannon) cross entropy.
Denote two distributions by `P` (`ref`) and `Q` (`other`). Assuming `P, Q`
are absolutely continuous with respect to one another and permit densities
`p(x) dr(x)` and `q(x) dr(x)`, (Shanon) cross entropy is defined as:
```none
H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
```
where `F` denotes the support of the random variable `X ~ P`.
Args:
ref: `tfd.Distribution` instance.
other: `tfd.Distribution` instance.
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` prepended to names of ops created by this function.
Returns:
cross_entropy: `ref.dtype` `Tensor` with shape `[B1, ..., Bn]`
representing `n` different calculations of (Shanon) cross entropy.
"""
with ops.name_scope(name, "cross_entropy"):
return ref.entropy() + kl_divergence(
ref, other, allow_nan_stats=allow_nan_stats)
@tf_export("distributions.RegisterKL")
class RegisterKL(object):
"""Decorator to register a KL divergence implementation function.
Usage:
@distributions.RegisterKL(distributions.Normal, distributions.Normal)
def _kl_normal_mvn(norm_a, norm_b):
# Return KL(norm_a || norm_b)
"""
@deprecation.deprecated(
"2019-01-01",
"The TensorFlow Distributions library has moved to "
"TensorFlow Probability "
"(https://github.com/tensorflow/probability). You "
"should update all references to use `tfp.distributions` "
"instead of `tf.distributions`.",
warn_once=True)
def __init__(self, dist_cls_a, dist_cls_b):
"""Initialize the KL registrar.
Args:
dist_cls_a: the class of the first argument of the KL divergence.
dist_cls_b: the class of the second argument of the KL divergence.
"""
self._key = (dist_cls_a, dist_cls_b)
def __call__(self, kl_fn):
"""Perform the KL registration.
Args:
kl_fn: The function to use for the KL divergence.
Returns:
kl_fn
Raises:
TypeError: if kl_fn is not a callable.
ValueError: if a KL divergence function has already been registered for
the given argument classes.
"""
if not callable(kl_fn):
raise TypeError("kl_fn must be callable, received: %s" % kl_fn)
if self._key in _DIVERGENCES:
raise ValueError("KL(%s || %s) has already been registered to: %s"
% (self._key[0].__name__, self._key[1].__name__,
_DIVERGENCES[self._key]))
_DIVERGENCES[self._key] = kl_fn
return kl_fn
|
