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power_transform.py
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/
power_transform.py
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# 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.
# ==============================================================================
"""PowerTransform bijector."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import ops
from tensorflow.python.framework import tensor_util
from tensorflow.python.ops import check_ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops.distributions import bijector
__all__ = [
"PowerTransform",
]
class PowerTransform(bijector.Bijector):
"""Compute `Y = g(X) = (1 + X * c)**(1 / c), X >= -1 / c`.
The [power transform](https://en.wikipedia.org/wiki/Power_transform) maps
inputs from `[0, inf]` to `[-1/c, inf]`; this is equivalent to the `inverse`
of this bijector.
This bijector is equivalent to the `Exp` bijector when `c=0`.
"""
def __init__(self,
power=0.,
event_ndims=0,
validate_args=False,
name="power_transform"):
"""Instantiates the `PowerTransform` bijector.
Args:
power: Python `float` scalar indicating the transform power, i.e.,
`Y = g(X) = (1 + X * c)**(1 / c)` where `c` is the `power`.
event_ndims: Python scalar indicating the number of dimensions associated
with a particular draw from the distribution.
validate_args: Python `bool` indicating whether arguments should be
checked for correctness.
name: Python `str` name given to ops managed by this object.
Raises:
ValueError: if `power < 0` or is not known statically.
"""
self._graph_parents = []
self._name = name
self._validate_args = validate_args
with self._name_scope("init", values=[power]):
power = tensor_util.constant_value(
ops.convert_to_tensor(power, name="power"))
if power is None or power < 0:
raise ValueError("`power` must be a non-negative TF constant.")
self._power = power
super(PowerTransform, self).__init__(
event_ndims=event_ndims,
validate_args=validate_args,
name=name)
@property
def power(self):
"""The `c` in: `Y = g(X) = (1 + X * c)**(1 / c)`."""
return self._power
def _forward(self, x):
x = self._maybe_assert_valid_x(x)
if self.power == 0.:
return math_ops.exp(x)
# If large x accuracy is an issue, consider using:
# (1. + x * self.power)**(1. / self.power) when x >> 1.
return math_ops.exp(math_ops.log1p(x * self.power) / self.power)
def _inverse(self, y):
y = self._maybe_assert_valid_y(y)
if self.power == 0.:
return math_ops.log(y)
# If large y accuracy is an issue, consider using:
# (y**self.power - 1.) / self.power when y >> 1.
return math_ops.expm1(math_ops.log(y) * self.power) / self.power
def _inverse_log_det_jacobian(self, y):
y = self._maybe_assert_valid_y(y)
event_dims = self._event_dims_tensor(y)
return (self.power - 1.) * math_ops.reduce_sum(
math_ops.log(y), axis=event_dims)
def _forward_log_det_jacobian(self, x):
x = self._maybe_assert_valid_x(x)
event_dims = self._event_dims_tensor(x)
if self.power == 0.:
return math_ops.reduce_sum(x, axis=event_dims)
return (1. / self.power - 1.) * math_ops.reduce_sum(
math_ops.log1p(x * self.power),
axis=event_dims)
def _maybe_assert_valid_x(self, x):
if not self.validate_args or self.power == 0.:
return x
is_valid = check_ops.assert_non_negative(
1. + self.power * x,
message="Forward transformation input must be at least {}.".format(
-1. / self.power))
return control_flow_ops.with_dependencies([is_valid], x)
def _maybe_assert_valid_y(self, y):
if not self.validate_args:
return y
is_valid = check_ops.assert_positive(
y, message="Inverse transformation input must be greater than 0.")
return control_flow_ops.with_dependencies([is_valid], y)