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logistic.py
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logistic.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.
# ============================================================================
"""The Logistic distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
# Dependency imports
import numpy as np
import tensorflow.compat.v2 as tf
from tensorflow_probability.python.bijectors import identity as identity_bijector
from tensorflow_probability.python.distributions import distribution
from tensorflow_probability.python.internal import assert_util
from tensorflow_probability.python.internal import dtype_util
from tensorflow_probability.python.internal import prefer_static
from tensorflow_probability.python.internal import reparameterization
from tensorflow_probability.python.internal import samplers
from tensorflow_probability.python.internal import tensor_util
class Logistic(distribution.Distribution):
"""The Logistic distribution with location `loc` and `scale` parameters.
#### Mathematical details
The cumulative density function of this distribution is:
```none
cdf(x; mu, sigma) = 1 / (1 + exp(-(x - mu) / sigma))
```
where `loc = mu` and `scale = sigma`.
The Logistic distribution is a member of the [location-scale family](
https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
constructed as,
```none
X ~ Logistic(loc=0, scale=1)
Y = loc + scale * X
```
#### Examples
Examples of initialization of one or a batch of distributions.
```python
tfd = tfp.distributions
# Define a single scalar Logistic distribution.
dist = tfd.Logistic(loc=0., scale=3.)
# Evaluate the cdf at 1, returning a scalar.
dist.cdf(1.)
# Define a batch of two scalar valued Logistics.
# The first has mean 1 and scale 11, the second 2 and 22.
dist = tfd.Logistic(loc=[1, 2.], scale=[11, 22.])
# Evaluate the pdf of the first distribution on 0, and the second on 1.5,
# returning a length two tensor.
dist.prob([0, 1.5])
# Get 3 samples, returning a 3 x 2 tensor.
dist.sample([3])
# Arguments are broadcast when possible.
# Define a batch of two scalar valued Logistics.
# Both have mean 1, but different scales.
dist = tfd.Logistic(loc=1., scale=[11, 22.])
# Evaluate the pdf of both distributions on the same point, 3.0,
# returning a length 2 tensor.
dist.prob(3.0)
```
"""
def __init__(self,
loc,
scale,
validate_args=False,
allow_nan_stats=True,
name='Logistic'):
"""Construct Logistic distributions with mean and scale `loc` and `scale`.
The parameters `loc` and `scale` must be shaped in a way that supports
broadcasting (e.g. `loc + scale` is a valid operation).
Args:
loc: Floating point tensor, the means of the distribution(s).
scale: Floating point tensor, the scales of the distribution(s). Must
contain only positive values.
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: The name to give Ops created by the initializer.
Raises:
TypeError: if loc and scale are different dtypes.
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
dtype = dtype_util.common_dtype([loc, scale], dtype_hint=tf.float32)
self._loc = tensor_util.convert_nonref_to_tensor(
loc, name='loc', dtype=dtype)
self._scale = tensor_util.convert_nonref_to_tensor(
scale, name='scale', dtype=dtype)
super(Logistic, self).__init__(
dtype=self._scale.dtype,
reparameterization_type=reparameterization.FULLY_REPARAMETERIZED,
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
parameters=parameters,
name=name)
@staticmethod
def _param_shapes(sample_shape):
return dict(
zip(('loc', 'scale'),
([tf.convert_to_tensor(sample_shape, dtype=tf.int32)] * 2)))
@classmethod
def _params_event_ndims(cls):
return dict(loc=0, scale=0)
@property
def loc(self):
"""Distribution parameter for the location."""
return self._loc
@property
def scale(self):
"""Distribution parameter for scale."""
return self._scale
def _batch_shape_tensor(self, loc=None, scale=None):
return prefer_static.broadcast_shape(
prefer_static.shape(self.loc if loc is None else loc),
prefer_static.shape(self.scale if scale is None else scale))
def _batch_shape(self):
return tf.broadcast_static_shape(self.loc.shape, self.scale.shape)
def _event_shape_tensor(self):
return tf.constant([], dtype=tf.int32)
def _event_shape(self):
return tf.TensorShape([])
def _sample_n(self, n, seed=None):
loc = tf.convert_to_tensor(self.loc)
scale = tf.convert_to_tensor(self.scale)
shape = tf.concat([[n], self._batch_shape_tensor(loc=loc, scale=scale)], 0)
# Uniform variates must be sampled from the open-interval `(0, 1)` rather
# than `[0, 1)`. To do so, we use
# `np.finfo(dtype_util.as_numpy_dtype(self.dtype)).tiny` because it is the
# smallest, positive, 'normal' number. A 'normal' number is such that the
# mantissa has an implicit leading 1. Normal, positive numbers x, y have the
# reasonable property that, `x + y >= max(x, y)`. In this case, a subnormal
# number (i.e., np.nextafter) can cause us to sample 0.
uniform = samplers.uniform(
shape=shape,
minval=np.finfo(dtype_util.as_numpy_dtype(self.dtype)).tiny,
maxval=1.,
dtype=self.dtype,
seed=seed)
sampled = tf.math.log(uniform) - tf.math.log1p(-uniform)
return sampled * scale + loc
def _log_prob(self, x):
loc = tf.convert_to_tensor(self.loc)
scale = tf.convert_to_tensor(self.scale)
z = (x - loc) / scale
return -z - 2. * tf.math.softplus(-z) - tf.math.log(scale)
def _log_cdf(self, x):
return -tf.math.softplus(-self._z(x))
def _cdf(self, x):
return tf.sigmoid(self._z(x))
def _log_survival_function(self, x):
return -tf.math.softplus(self._z(x))
def _survival_function(self, x):
return tf.sigmoid(-self._z(x))
def _entropy(self):
scale = tf.convert_to_tensor(self.scale)
return tf.broadcast_to(2. + tf.math.log(scale),
self._batch_shape_tensor(scale=scale))
def _mean(self):
loc = tf.convert_to_tensor(self.loc)
return tf.broadcast_to(loc, self._batch_shape_tensor(loc=loc))
def _stddev(self):
scale = tf.convert_to_tensor(self.scale)
return tf.broadcast_to(
scale * tf.constant(np.pi / np.sqrt(3), dtype=scale.dtype),
self._batch_shape_tensor(scale=scale))
def _mode(self):
return self._mean()
def _z(self, x):
"""Standardize input `x` to a unit logistic."""
with tf.name_scope('standardize'):
return (x - self.loc) / self.scale
def _quantile(self, x):
return self.loc + self.scale * (tf.math.log(x) - tf.math.log1p(-x))
def _default_event_space_bijector(self):
return identity_bijector.Identity(validate_args=self.validate_args)
def _parameter_control_dependencies(self, is_init):
if is_init:
dtype_util.assert_same_float_dtype([self.loc, self.scale])
if not self.validate_args:
return []
assertions = []
if is_init != tensor_util.is_ref(self._scale):
assertions.append(assert_util.assert_positive(
self._scale, message='Argument `scale` must be positive.'))
return assertions