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gumbel.py
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gumbel.py
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# Copyright (c) 2022 PaddlePaddle 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.
import math
import numbers
import numpy as np
import paddle
from paddle.distribution.transformed_distribution import TransformedDistribution
from paddle.fluid import framework
class Gumbel(TransformedDistribution):
r"""The Gumbel distribution with location `loc` and `scale` parameters.
Mathematical details
The probability density function (pdf) is
.. math::
pdf(x; mu, sigma) = exp(-(x - mu) / sigma - exp(-(x - mu) / sigma)) / sigma
In the above equation:
* :math:`loc = \mu`: is the mean.
* :math:`scale = \sigma`: is the std.
Args:
loc(int|float|tensor): The mean of gumbel distribution.The data type is int, float, tensor.
scale(int|float|tensor): The std of gumbel distribution.The data type is int, float, tensor.
Examples:
.. code-block:: python
import paddle
from paddle.distribution.gumbel import Gumbel
# Gumbel distributed with loc=0, scale=1
dist = Gumbel(paddle.full([1], 0.0), paddle.full([1], 1.0))
dist.sample([2])
# Tensor(shape=[2, 1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [[-0.27544352], [-0.64499271]])
value = paddle.full([1], 0.5)
dist.prob(value)
# Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [0.33070430])
dist.log_prob(value)
# Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [-1.10653067])
dist.cdf(value)
# Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [0.54523915])
dist.entropy()
# Tensor(shape=[1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [1.57721567])
dist.rsample([2])
# Tensor(shape=[2, 1], dtype=float32, place=Place(gpu:0), stop_gradient=True, [[0.80463481], [0.91893655]])
"""
def __init__(self, loc, scale):
if not isinstance(loc, (numbers.Real, framework.Variable)):
raise TypeError(
f"Expected type of loc is Real|Variable, but got {type(loc)}"
)
if not isinstance(scale, (numbers.Real, framework.Variable)):
raise TypeError(
f"Expected type of scale is Real|Variable, but got {type(scale)}"
)
if isinstance(loc, numbers.Real):
loc = paddle.full(shape=(), fill_value=loc)
if isinstance(scale, numbers.Real):
scale = paddle.full(shape=(), fill_value=scale)
if loc.shape != scale.shape:
self.loc, self.scale = paddle.broadcast_tensors([loc, scale])
else:
self.loc, self.scale = loc, scale
finfo = np.finfo(dtype='float32')
self.base_dist = paddle.distribution.Uniform(
paddle.full_like(self.loc, float(finfo.tiny)),
paddle.full_like(self.loc, float(1 - finfo.eps)),
)
self.transforms = ()
super().__init__(self.base_dist, self.transforms)
@property
def mean(self):
r"""Mean of distribution
The mean is
.. math::
mean = \mu + \sigma * γ
In the above equation:
* :math:`loc = \mu`: is the location parameter.
* :math:`scale = \sigma`: is the scale parameter.
* :math:`γ`: is the euler's constant.
Returns:
Tensor: mean value.
"""
return self.loc + self.scale * np.euler_gamma
@property
def variance(self):
r"""Variance of distribution.
The variance is
.. math::
variance = \sigma^2 * \pi^2 / 6
In the above equation:
* :math:`scale = \sigma`: is the scale parameter.
Returns:
Tensor: The variance value.
"""
temp = paddle.full(
shape=self.loc.shape,
fill_value=math.pi * math.pi,
dtype=self.scale.dtype,
)
return paddle.pow(self.scale, 2) * temp / 6
@property
def stddev(self):
r"""Standard deviation of distribution
The standard deviation is
.. math::
stddev = \sqrt{\sigma^2 * \pi^2 / 6}
In the above equation:
* :math:`scale = \sigma`: is the scale parameter.
Returns:
Tensor: std value
"""
return paddle.sqrt(self.variance)
def prob(self, value):
"""Probability density/mass function
Args:
value (Tensor): The input tensor.
Returns:
Tensor: probability.The data type is same with value.
"""
y = (self.loc - value) / self.scale
return paddle.exp(y - paddle.exp(y)) / self.scale
def log_prob(self, value):
"""Log probability density/mass function.
Args:
value (Tensor): The input tensor.
Returns:
Tensor: log probability.The data type is same with value.
"""
return paddle.log(self.prob(value))
def cdf(self, value):
"""Cumulative distribution function.
Args:
value (Tensor): value to be evaluated.
Returns:
Tensor: cumulative probability of value.
"""
return paddle.exp(-paddle.exp(-(value - self.loc) / self.scale))
def entropy(self):
"""Entropy of Gumbel distribution.
Returns:
Entropy of distribution.
"""
return paddle.log(self.scale) + 1 + np.euler_gamma
def sample(self, shape):
"""Sample from ``Gumbel``.
Args:
shape (Sequence[int], optional): The sample shape. Defaults to ().
Returns:
Tensor: A tensor with prepended dimensions shape.The data type is float32.
"""
with paddle.no_grad():
return self.rsample(shape)
def rsample(self, shape):
"""reparameterized sample
Args:
shape (Sequence[int]): 1D `int32`. Shape of the generated samples.
Returns:
Tensor: A tensor with prepended dimensions shape.The data type is float32.
"""
exp_trans = paddle.distribution.ExpTransform()
affine_trans_1 = paddle.distribution.AffineTransform(
paddle.full(
shape=self.scale.shape, fill_value=0, dtype=self.loc.dtype
),
-paddle.ones_like(self.scale),
)
affine_trans_2 = paddle.distribution.AffineTransform(
self.loc, -self.scale
)
return affine_trans_2.forward(
exp_trans.inverse(
affine_trans_1.forward(
exp_trans.inverse(self._base.sample(shape))
)
)
)