# 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.
import math
from typing import Dict, List, Optional, Tuple
import numpy as np
from gluonts.core.component import validated
from gluonts.mx import Tensor
from .distribution import (
Distribution,
_sample_multiple,
getF,
nans_like,
softplus,
)
from .distribution_output import DistributionOutput
[docs]class StudentT(Distribution):
r"""
Student's t-distribution.
Parameters
----------
mu
Tensor containing the means, of shape `(*batch_shape, *event_shape)`.
sigma
Tensor containing the standard deviations, of shape
`(*batch_shape, *event_shape)`.
nu
Nonnegative tensor containing the degrees of freedom of the
distribution, of shape `(*batch_shape, *event_shape)`.
F
"""
is_reparameterizable = False
@validated()
def __init__(self, mu: Tensor, sigma: Tensor, nu: Tensor, F=None) -> None:
self.mu = mu
self.sigma = sigma
self.nu = nu
@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
@property
def mean(self) -> Tensor:
return self.F.where(self.nu > 1.0, self.mu, nans_like(self.mu))
@property
def stddev(self) -> Tensor:
F = self.F
mu, nu, sigma = self.mu, self.nu, self.sigma
return F.where(nu > 2.0, sigma * F.sqrt(nu / (nu - 2)), nans_like(mu))
[docs] def log_prob(self, x: Tensor) -> Tensor:
mu, sigma, nu = self.mu, self.sigma, self.nu
F = self.F
nup1_half = (nu + 1.0) / 2.0
part1 = 1.0 / nu * F.square((x - mu) / sigma)
Z = (
F.gammaln(nup1_half)
- F.gammaln(nu / 2.0)
- 0.5 * F.log(math.pi * nu)
- F.log(sigma)
)
ll = Z - nup1_half * F.log1p(part1)
return ll
[docs] def sample(
self, num_samples: Optional[int] = None, dtype=np.float32
) -> Tensor:
def s(mu: Tensor, sigma: Tensor, nu: Tensor) -> Tensor:
F = self.F
gammas = F.sample_gamma(
alpha=nu / 2.0, beta=2.0 / (nu * F.square(sigma)), dtype=dtype
)
normal = F.sample_normal(
mu=mu, sigma=1.0 / F.sqrt(gammas), dtype=dtype
)
return normal
return _sample_multiple(
s,
mu=self.mu,
sigma=self.sigma,
nu=self.nu,
num_samples=num_samples,
)
@property
def args(self) -> List:
return [self.mu, self.sigma, self.nu]
[docs]class StudentTOutput(DistributionOutput):
args_dim: Dict[str, int] = {"mu": 1, "sigma": 1, "nu": 1}
distr_cls: type = StudentT
[docs] @classmethod
def domain_map(cls, F, mu, sigma, nu):
sigma = F.maximum(softplus(F, sigma), cls.eps())
nu = 2.0 + F.maximum(softplus(F, nu), cls.eps())
return mu.squeeze(axis=-1), sigma.squeeze(axis=-1), nu.squeeze(axis=-1)
@property
def event_shape(self) -> Tuple:
return ()