150 lines
5.1 KiB
Python
150 lines
5.1 KiB
Python
# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""The Exponential distribution class."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import numpy as np
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from tensorflow.python.framework import dtypes
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from tensorflow.python.framework import ops
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import math_ops
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from tensorflow.python.ops import nn
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from tensorflow.python.ops import random_ops
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from tensorflow.python.ops.distributions import gamma
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from tensorflow.python.util.tf_export import tf_export
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__all__ = [
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"Exponential",
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"ExponentialWithSoftplusRate",
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]
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@tf_export("distributions.Exponential")
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class Exponential(gamma.Gamma):
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"""Exponential distribution.
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The Exponential distribution is parameterized by an event `rate` parameter.
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#### Mathematical Details
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The probability density function (pdf) is,
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```none
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pdf(x; lambda, x > 0) = exp(-lambda x) / Z
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Z = 1 / lambda
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```
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where `rate = lambda` and `Z` is the normalizaing constant.
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The Exponential distribution is a special case of the Gamma distribution,
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i.e.,
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```python
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Exponential(rate) = Gamma(concentration=1., rate)
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```
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The Exponential distribution uses a `rate` parameter, or "inverse scale",
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which can be intuited as,
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```none
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X ~ Exponential(rate=1)
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Y = X / rate
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```
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"""
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def __init__(self,
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rate,
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validate_args=False,
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allow_nan_stats=True,
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name="Exponential"):
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"""Construct Exponential distribution with parameter `rate`.
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Args:
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rate: Floating point tensor, equivalent to `1 / mean`. Must contain only
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positive values.
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validate_args: Python `bool`, default `False`. When `True` distribution
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parameters are checked for validity despite possibly degrading runtime
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performance. When `False` invalid inputs may silently render incorrect
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outputs.
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allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
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(e.g., mean, mode, variance) use the value "`NaN`" to indicate the
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result is undefined. When `False`, an exception is raised if one or
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more of the statistic's batch members are undefined.
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name: Python `str` name prefixed to Ops created by this class.
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"""
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parameters = dict(locals())
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# Even though all statistics of are defined for valid inputs, this is not
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# true in the parent class "Gamma." Therefore, passing
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# allow_nan_stats=True
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# through to the parent class results in unnecessary asserts.
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with ops.name_scope(name, values=[rate]) as name:
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self._rate = ops.convert_to_tensor(rate, name="rate")
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super(Exponential, self).__init__(
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concentration=array_ops.ones([], dtype=self._rate.dtype),
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rate=self._rate,
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allow_nan_stats=allow_nan_stats,
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validate_args=validate_args,
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name=name)
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self._parameters = parameters
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self._graph_parents += [self._rate]
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@staticmethod
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def _param_shapes(sample_shape):
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return {"rate": ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)}
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@property
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def rate(self):
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return self._rate
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def _sample_n(self, n, seed=None):
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shape = array_ops.concat([[n], array_ops.shape(self._rate)], 0)
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# Uniform variates must be sampled from the open-interval `(0, 1)` rather
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# than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
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# because it is the smallest, positive, "normal" number. A "normal" number
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# is such that the mantissa has an implicit leading 1. Normal, positive
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# numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
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# this case, a subnormal number (i.e., np.nextafter) can cause us to sample
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# 0.
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sampled = random_ops.random_uniform(
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shape,
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minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
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maxval=1.,
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seed=seed,
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dtype=self.dtype)
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return -math_ops.log(sampled) / self._rate
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class ExponentialWithSoftplusRate(Exponential):
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"""Exponential with softplus transform on `rate`."""
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def __init__(self,
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rate,
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validate_args=False,
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allow_nan_stats=True,
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name="ExponentialWithSoftplusRate"):
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parameters = dict(locals())
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with ops.name_scope(name, values=[rate]) as name:
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super(ExponentialWithSoftplusRate, self).__init__(
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rate=nn.softplus(rate, name="softplus_rate"),
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validate_args=validate_args,
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allow_nan_stats=allow_nan_stats,
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name=name)
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self._parameters = parameters
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