# Copyright 2018 Amazon.com, Inc. or its affiliates. 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.
# A copy of the License is located at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# or in the "license" file accompanying this file. This file 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.
from typing import Dict, List, Tuple
import numpy as np
from gluonts.core.component import validated
from gluonts.mx import Tensor
from .distribution import Distribution, _sample_multiple, getF, softplus
from .distribution_output import DistributionOutput
[docs]class Laplace(Distribution):
r"""
Laplace distribution.
Parameters
----------
mu
Tensor containing the means, of shape `(*batch_shape, *event_shape)`.
b
Tensor containing the distribution scale, of shape
`(*batch_shape, *event_shape)`.
F
"""
is_reparameterizable = True
@validated()
def __init__(self, mu: Tensor, b: Tensor) -> None:
self.mu = mu
self.b = b
@property
def F(self):
return getF(self.mu)
@property
def batch_shape(self) -> Tuple:
return self.mu.shape
@property
def event_shape(self) -> Tuple:
return ()
@property
def event_dim(self) -> int:
return 0
[docs] def log_prob(self, x: Tensor) -> Tensor:
F = self.F
return -1.0 * (F.log(2.0 * self.b) + F.abs((x - self.mu) / self.b))
@property
def mean(self) -> Tensor:
return self.mu
@property
def stddev(self) -> Tensor:
return 2.0**0.5 * self.b
[docs] def cdf(self, x: Tensor) -> Tensor:
y = (x - self.mu) / self.b
return 0.5 + 0.5 * y.sign() * (1.0 - self.F.exp(-y.abs()))
[docs] def sample_rep(self, num_samples=None, dtype=np.float32) -> Tensor:
F = self.F
def s(mu: Tensor, b: Tensor) -> Tensor:
ones = mu.ones_like()
x = F.random.uniform(-0.5 * ones, 0.5 * ones, dtype=dtype)
laplace_samples = mu - b * F.sign(x) * F.log(
(1.0 - 2.0 * F.abs(x)).clip(1.0e-30, 1.0e30)
# 1.0 - 2.0 * F.abs(x)
)
return laplace_samples
return _sample_multiple(
s, mu=self.mu, b=self.b, num_samples=num_samples
)
[docs] def quantile(self, level: Tensor) -> Tensor:
F = self.F
for _ in range(self.all_dim):
level = level.expand_dims(axis=-1)
condition = F.broadcast_greater(level, level.zeros_like() + 0.5)
u = F.where(condition, F.log(2.0 * level), -F.log(2.0 - 2.0 * level))
return F.broadcast_add(self.mu, F.broadcast_mul(self.b, u))
@property
def args(self) -> List:
return [self.mu, self.b]
[docs]class LaplaceOutput(DistributionOutput):
args_dim: Dict[str, int] = {"mu": 1, "b": 1}
distr_cls: type = Laplace
[docs] @classmethod
def domain_map(cls, F, mu, b):
b = F.maximum(softplus(F, b), cls.eps())
return mu.squeeze(axis=-1), b.squeeze(axis=-1)
@property
def event_shape(self) -> Tuple:
return ()
[docs]class LaplaceFixedVarianceOutput(LaplaceOutput):
[docs] @classmethod
def domain_map(cls, F, mu, b):
b = 0.01 * F.ones_like(b)
return mu.squeeze(axis=-1), b.squeeze(axis=-1)