bca5e7385f
Explicit constructor call is no less clear and match what we export via the public API. The functions will be removed once all the internal users are migrated. PiperOrigin-RevId: 259620054
296 lines
9.6 KiB
Python
296 lines
9.6 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 Normal (Gaussian) 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 math
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from tensorflow.python.framework import constant_op
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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.framework import tensor_shape
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import check_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 distribution
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from tensorflow.python.ops.distributions import kullback_leibler
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from tensorflow.python.ops.distributions import special_math
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from tensorflow.python.util import deprecation
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from tensorflow.python.util.tf_export import tf_export
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__all__ = [
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"Normal",
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"NormalWithSoftplusScale",
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]
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@tf_export(v1=["distributions.Normal"])
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class Normal(distribution.Distribution):
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"""The Normal distribution with location `loc` and `scale` parameters.
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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; mu, sigma) = exp(-0.5 (x - mu)**2 / sigma**2) / Z
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Z = (2 pi sigma**2)**0.5
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```
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where `loc = mu` is the mean, `scale = sigma` is the std. deviation, and, `Z`
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is the normalization constant.
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The Normal distribution is a member of the [location-scale family](
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https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
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constructed as,
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```none
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X ~ Normal(loc=0, scale=1)
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Y = loc + scale * X
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```
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#### Examples
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Examples of initialization of one or a batch of distributions.
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```python
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import tensorflow_probability as tfp
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tfd = tfp.distributions
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# Define a single scalar Normal distribution.
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dist = tfd.Normal(loc=0., scale=3.)
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# Evaluate the cdf at 1, returning a scalar.
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dist.cdf(1.)
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# Define a batch of two scalar valued Normals.
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# The first has mean 1 and standard deviation 11, the second 2 and 22.
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dist = tfd.Normal(loc=[1, 2.], scale=[11, 22.])
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# Evaluate the pdf of the first distribution on 0, and the second on 1.5,
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# returning a length two tensor.
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dist.prob([0, 1.5])
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# Get 3 samples, returning a 3 x 2 tensor.
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dist.sample([3])
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```
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Arguments are broadcast when possible.
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```python
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# Define a batch of two scalar valued Normals.
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# Both have mean 1, but different standard deviations.
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dist = tfd.Normal(loc=1., scale=[11, 22.])
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# Evaluate the pdf of both distributions on the same point, 3.0,
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# returning a length 2 tensor.
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dist.prob(3.0)
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```
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"""
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@deprecation.deprecated(
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"2019-01-01",
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"The TensorFlow Distributions library has moved to "
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"TensorFlow Probability "
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"(https://github.com/tensorflow/probability). You "
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"should update all references to use `tfp.distributions` "
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"instead of `tf.distributions`.",
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warn_once=True)
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def __init__(self,
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loc,
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scale,
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validate_args=False,
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allow_nan_stats=True,
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name="Normal"):
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"""Construct Normal distributions with mean and stddev `loc` and `scale`.
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The parameters `loc` and `scale` must be shaped in a way that supports
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broadcasting (e.g. `loc + scale` is a valid operation).
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Args:
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loc: Floating point tensor; the means of the distribution(s).
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scale: Floating point tensor; the stddevs of the distribution(s).
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Must contain only 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`,
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statistics (e.g., mean, mode, variance) use the value "`NaN`" to
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indicate the result is undefined. When `False`, an exception is raised
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if one or 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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Raises:
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TypeError: if `loc` and `scale` have different `dtype`.
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"""
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parameters = dict(locals())
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with ops.name_scope(name, values=[loc, scale]) as name:
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with ops.control_dependencies([check_ops.assert_positive(scale)] if
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validate_args else []):
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self._loc = array_ops.identity(loc, name="loc")
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self._scale = array_ops.identity(scale, name="scale")
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check_ops.assert_same_float_dtype([self._loc, self._scale])
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super(Normal, self).__init__(
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dtype=self._scale.dtype,
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reparameterization_type=distribution.FULLY_REPARAMETERIZED,
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validate_args=validate_args,
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allow_nan_stats=allow_nan_stats,
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parameters=parameters,
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graph_parents=[self._loc, self._scale],
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name=name)
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@staticmethod
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def _param_shapes(sample_shape):
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return dict(
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zip(("loc", "scale"), ([ops.convert_to_tensor(
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sample_shape, dtype=dtypes.int32)] * 2)))
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@property
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def loc(self):
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"""Distribution parameter for the mean."""
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return self._loc
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@property
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def scale(self):
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"""Distribution parameter for standard deviation."""
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return self._scale
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def _batch_shape_tensor(self):
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return array_ops.broadcast_dynamic_shape(
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array_ops.shape(self.loc),
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array_ops.shape(self.scale))
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def _batch_shape(self):
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return array_ops.broadcast_static_shape(
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self.loc.get_shape(),
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self.scale.get_shape())
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def _event_shape_tensor(self):
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return constant_op.constant([], dtype=dtypes.int32)
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def _event_shape(self):
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return tensor_shape.TensorShape([])
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def _sample_n(self, n, seed=None):
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shape = array_ops.concat([[n], self.batch_shape_tensor()], 0)
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sampled = random_ops.random_normal(
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shape=shape, mean=0., stddev=1., dtype=self.loc.dtype, seed=seed)
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return sampled * self.scale + self.loc
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def _log_prob(self, x):
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return self._log_unnormalized_prob(x) - self._log_normalization()
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def _log_cdf(self, x):
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return special_math.log_ndtr(self._z(x))
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def _cdf(self, x):
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return special_math.ndtr(self._z(x))
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def _log_survival_function(self, x):
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return special_math.log_ndtr(-self._z(x))
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def _survival_function(self, x):
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return special_math.ndtr(-self._z(x))
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def _log_unnormalized_prob(self, x):
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return -0.5 * math_ops.square(self._z(x))
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def _log_normalization(self):
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return 0.5 * math.log(2. * math.pi) + math_ops.log(self.scale)
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def _entropy(self):
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# Use broadcasting rules to calculate the full broadcast scale.
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scale = self.scale * array_ops.ones_like(self.loc)
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return 0.5 * math.log(2. * math.pi * math.e) + math_ops.log(scale)
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def _mean(self):
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return self.loc * array_ops.ones_like(self.scale)
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def _quantile(self, p):
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return self._inv_z(special_math.ndtri(p))
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def _stddev(self):
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return self.scale * array_ops.ones_like(self.loc)
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def _mode(self):
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return self._mean()
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def _z(self, x):
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"""Standardize input `x` to a unit normal."""
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with ops.name_scope("standardize", values=[x]):
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return (x - self.loc) / self.scale
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def _inv_z(self, z):
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"""Reconstruct input `x` from a its normalized version."""
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with ops.name_scope("reconstruct", values=[z]):
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return z * self.scale + self.loc
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class NormalWithSoftplusScale(Normal):
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"""Normal with softplus applied to `scale`."""
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@deprecation.deprecated(
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"2019-01-01",
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"Use `tfd.Normal(loc, tf.nn.softplus(scale)) "
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"instead.",
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warn_once=True)
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def __init__(self,
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loc,
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scale,
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validate_args=False,
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allow_nan_stats=True,
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name="NormalWithSoftplusScale"):
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parameters = dict(locals())
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with ops.name_scope(name, values=[scale]) as name:
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super(NormalWithSoftplusScale, self).__init__(
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loc=loc,
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scale=nn.softplus(scale, name="softplus_scale"),
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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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@kullback_leibler.RegisterKL(Normal, Normal)
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def _kl_normal_normal(n_a, n_b, name=None):
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"""Calculate the batched KL divergence KL(n_a || n_b) with n_a and n_b Normal.
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Args:
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n_a: instance of a Normal distribution object.
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n_b: instance of a Normal distribution object.
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name: (optional) Name to use for created operations.
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default is "kl_normal_normal".
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Returns:
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Batchwise KL(n_a || n_b)
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"""
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with ops.name_scope(name, "kl_normal_normal", [n_a.loc, n_b.loc]):
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one = constant_op.constant(1, dtype=n_a.dtype)
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two = constant_op.constant(2, dtype=n_a.dtype)
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half = constant_op.constant(0.5, dtype=n_a.dtype)
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s_a_squared = math_ops.square(n_a.scale)
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s_b_squared = math_ops.square(n_b.scale)
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ratio = s_a_squared / s_b_squared
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return (math_ops.squared_difference(n_a.loc, n_b.loc) / (two * s_b_squared)
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+ half * (ratio - one - math_ops.log(ratio)))
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