Table Of Contents
Table Of Contents

Source code for gluonts.distribution.student_t

# 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.

# Standard library imports
import math
from typing import Dict, Optional, Tuple, List

# Third-party imports
import numpy as np

# First-party imports
from gluonts.model.common import Tensor
from gluonts.core.component import validated

# Relative imports
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 self.F = F if F else getF(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 = softplus(F, sigma) nu = 2.0 + softplus(F, nu) return mu.squeeze(axis=-1), sigma.squeeze(axis=-1), nu.squeeze(axis=-1)
@property def event_shape(self) -> Tuple: return ()