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gev_cdf.py
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gev_cdf.py
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# Copyright 2020 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.
# ============================================================================
"""GeneralizedExtremeValue bijector."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import tensorflow.compat.v2 as tf
from tensorflow_probability.python.bijectors import bijector
from tensorflow_probability.python.bijectors import softplus as softplus_bijector
from tensorflow_probability.python.internal import assert_util
from tensorflow_probability.python.internal import dtype_util
from tensorflow_probability.python.internal import parameter_properties
from tensorflow_probability.python.internal import tensor_util
__all__ = [
'GeneralizedExtremeValueCDF',
]
class GeneralizedExtremeValueCDF(bijector.AutoCompositeTensorBijector):
"""Compute the GeneralizedExtremeValue CDF.
Compute `Y = g(X) = exp(-t(X))`,
where `t(x)` is defined to be:
*`(1 + conc * (x - loc) / scale) ) ** (-1 / conc)` when `conc != 0`;
*`exp(-(x - loc) / scale)` when `conc = 0`.
This bijector maps inputs from the domain to `[0, 1]`, where the domain is
* [loc - scale/conc, inf) when conc > 0;
* (-inf, loc - scale/conc] when conc < 0;
* (-inf, inf) when conc = 0;
The inverse of the bijector applied to a uniform random variable
`X ~ U(0, 1)` gives back a random variable with the
[Generalized extreme value distribution](
https://https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution):
When `concentration -> +-inf`, the probability mass concentrates near `loc`.
```none
Y ~ GeneralizedExtremeValueCDF(loc, scale, conc)
pdf(y; loc, scale, conc) = t(y; loc, scale, conc) ** (1 + conc) * exp(
- t(y; loc, scale, conc) ) / scale
where t(x) =
* (1 + conc * (x - loc) / scale) ) ** (-1 / conc) when conc != 0;
* exp(-(x - loc) / scale) when conc = 0.
```
"""
def __init__(self,
loc=0.,
scale=1.,
concentration=0,
validate_args=False,
name='generalizedextremevalue_cdf'):
"""Instantiates the `GeneralizedExtremeValueCDF` bijector.
Args:
loc: Float-like `Tensor` that is the same dtype and is broadcastable with
`scale` and `concentration`.
scale: Positive Float-like `Tensor` that is the same dtype and is
broadcastable with `loc` and `concentration`.
concentration: Nonzero float-like `Tensor` that is the same dtype and is
broadcastable with `loc` and `scale`.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
name: Python `str` name given to ops managed by this object.
"""
parameters = dict(locals())
with tf.name_scope(name) as name:
dtype = dtype_util.common_dtype([loc, scale, concentration],
dtype_hint=tf.float32)
self._loc = tensor_util.convert_nonref_to_tensor(
loc, dtype=dtype, name='loc')
self._scale = tensor_util.convert_nonref_to_tensor(
scale, dtype=dtype, name='scale')
self._concentration = tensor_util.convert_nonref_to_tensor(
concentration, dtype=dtype, name='concentration')
super(GeneralizedExtremeValueCDF, self).__init__(
validate_args=validate_args,
forward_min_event_ndims=0,
parameters=parameters,
name=name)
@classmethod
def _parameter_properties(cls, dtype):
return dict(
loc=parameter_properties.ParameterProperties(),
scale=parameter_properties.ParameterProperties(
default_constraining_bijector_fn=(
lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype)))),
concentration=parameter_properties.ParameterProperties(
default_constraining_bijector_fn=(
lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype)))))
@property
def loc(self):
"""The location parameter in the Generalized Extreme Value CDF."""
return self._loc
@property
def scale(self):
"""The scale parameter in the Generalized Extreme Value CDF."""
return self._scale
@property
def concentration(self):
"""The concentration parameter in the Generalized Extreme Value CDF."""
return self._concentration
@classmethod
def _is_increasing(cls):
return True
def _forward(self, x):
loc = tf.convert_to_tensor(self.loc)
scale = tf.convert_to_tensor(self.scale)
conc = tf.convert_to_tensor(self.concentration)
with tf.control_dependencies(
self._maybe_assert_valid_x(
x, loc=loc, scale=scale, concentration=conc)):
z = (x - loc) / scale
equal_zero = tf.equal(conc, 0.)
# deal with case that gradient is N/A when conc = 0
safe_conc = tf.where(equal_zero, tf.ones_like(conc), conc)
t = tf.where(
equal_zero, tf.math.exp(-z),
tf.math.exp(-tf.math.log1p(z * safe_conc) / safe_conc))
return tf.exp(-t)
def _inverse(self, y):
with tf.control_dependencies(self._maybe_assert_valid_y(y)):
t = -tf.math.log(y)
conc = tf.convert_to_tensor(self.concentration)
equal_zero = tf.equal(conc, 0.)
# deal with case that gradient is N/A when conc = 0
safe_conc = tf.where(equal_zero, tf.ones_like(conc), conc)
z = tf.where(
equal_zero, -tf.math.log(t),
tf.math.expm1(-tf.math.log(t) * safe_conc) / safe_conc)
return self.loc + self.scale * z
def _forward_log_det_jacobian(self, x):
loc = tf.convert_to_tensor(self.loc)
scale = tf.convert_to_tensor(self.scale)
conc = tf.convert_to_tensor(self.concentration)
with tf.control_dependencies(
self._maybe_assert_valid_x(
x, loc=loc, scale=scale, concentration=conc)):
z = (x - loc) / scale
equal_zero = tf.equal(conc, 0.)
# deal with case that gradient is N/A when conc = 0
safe_conc = tf.where(equal_zero, tf.ones_like(conc), conc)
log_t = tf.where(
equal_zero, -z,
-tf.math.log1p(z * safe_conc) / safe_conc)
return (tf.math.multiply_no_nan(conc + 1., log_t) -
tf.math.exp(log_t) - tf.math.log(scale))
def _inverse_log_det_jacobian(self, y):
with tf.control_dependencies(self._maybe_assert_valid_y(y)):
t = -tf.math.log(y)
log_dt = tf.math.xlogy(-self.concentration - 1., t)
return tf.math.log(self.scale / y) + log_dt
def _maybe_assert_valid_x(self, x, loc=None, scale=None, concentration=None):
if not self.validate_args:
return []
loc = tf.convert_to_tensor(self.loc) if loc is None else loc
scale = tf.convert_to_tensor(self.scale) if scale is None else scale
concentration = (
tf.convert_to_tensor(self.concentration) if concentration is None else
concentration)
# We intentionally compute the boundary with (1.0 / concentration) * scale
# instead of just scale / concentration.
# Why? The sampler returns loc + (foo / concentration) * scale,
# and at high-ish values of concentration, foo has a decent
# probability of being numerically exactly -1. We therefore mimic
# the pattern of round-off that occurs in the sampler to make sure
# that samples emitted from this distribution will pass its own
# validations. This is sometimes necessary: in TF's float32,
# 0.69314826 / 37.50019 < (1.0 / 37.50019) * 0.69314826
boundary = loc - (1.0 / concentration) * scale
# The support of this bijector depends on the sign of concentration.
is_in_bounds = tf.where(concentration > 0., x >= boundary, x <= boundary)
# For concentration 0, the domain is the whole line.
is_in_bounds = is_in_bounds | tf.math.equal(concentration, 0.)
return [
assert_util.assert_equal(
is_in_bounds,
True,
message='Forward transformation input must be inside domain.')
]
def _maybe_assert_valid_y(self, y):
if not self.validate_args:
return []
is_positive = assert_util.assert_non_negative(
y, message='Inverse transformation input must be greater than 0.')
less_than_one = assert_util.assert_less_equal(
y,
tf.constant(1., y.dtype),
message='Inverse transformation input must be less than or equal to 1.')
return [is_positive, less_than_one]
def _parameter_control_dependencies(self, is_init):
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