Source code for gluonts.model.tpp.distribution.loglogistic

# Copyright 2018 Amazon.com, Inc. or its affiliates. All Rights Reserved.
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# 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
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#     http://www.apache.org/licenses/LICENSE-2.0
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# 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
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from typing import Dict, Optional, Tuple

import numpy as np
from mxnet import autograd, nd

from gluonts.core.component import validated
from gluonts.mx import Tensor
from gluonts.mx.distribution.distribution import getF

from .base import TPPDistribution, TPPDistributionOutput


[docs]class Loglogistic(TPPDistribution): r""" Log-logistic distribution. A very heavy-tailed distribution over positive real numbers. https://en.wikipedia.org/wiki/Log-logistic_distribution Drawing :math:`x \sim \operatorname{Loglogistic}(\mu, \sigma)` is equivalent to: .. math:: y &\sim \operatorname{Logistic}(\mu, \sigma)\\ x &= \exp(y) """ is_reparametrizable = True @validated() def __init__(self, mu: Tensor, sigma: Tensor) -> None: self.mu = mu self.sigma = sigma @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: result = ( self.mu.exp() * self.sigma * np.pi / (self.sigma * np.pi).sin() ) # Expectation diverges if sigma > 1 return nd.where( self.sigma > 1.0, nd.full(result.shape, np.inf), result )
[docs] def log_intensity(self, x: Tensor) -> Tensor: r""" Logarithm of the intensity (a.k.a. hazard) function. The intensity is defined as :math:`\lambda(x) = p(x) / S(x)`. We define :math:`z = (\log(x) - \mu) / \sigma` and obtain the intensity as :math:`\lambda(x) = sigmoid(z) / (\sigma * \log(x))`, or equivalently :math:`\log \lambda(x) = z - \log(1 + \exp(z)) - \log(\sigma) - \log(x)`. """ log_x = x.clip(1e-20, np.inf).log() z = (log_x - self.mu) / self.sigma F = getF(x) return z - self.sigma.log() - F.Activation(z, "softrelu") - log_x
[docs] def log_survival(self, x: Tensor) -> Tensor: r""" Logarithm of the survival function :math:`\log S(x) = \log(1 - CDF(x))`. We define :math:`z = (\log(x) - \mu) / \sigma` and obtain the survival function as :math:`S(x) = sigmoid(-z)`, or equivalently :math:`\log S(x) = -\log(1 + \exp(z))`. """ log_x = x.clip(1e-20, np.inf).log() z = (log_x - self.mu) / self.sigma F = getF(x) return -F.Activation(z, "softrelu")
[docs] def log_prob(self, x: Tensor) -> Tensor: return self.log_intensity(x) + self.log_survival(x)
[docs] def sample( self, num_samples=None, dtype=np.float32, lower_bound: Optional[Tensor] = None, ) -> Tensor: r""" Draw samples from the distribution. We generate samples as :math:`u \sim Uniform(0, 1), x = S^{-1}(u)`, where :math:`S^{-1}` is the inverse of the survival function :math:`S(x) = 1 - CDF(x)`. Parameters ---------- num_samples Number of samples to generate. dtype Data type of the generated samples. lower_bound If None, generate samples as usual. If lower_bound is provided, all generated samples will be larger than the specified values. That is, we sample from `p(x | x > lower_bound)`. Shape: `(*batch_size)` Returns ------- x Sampled inter-event times. Shape: `(num_samples, *batch_size)` """ F = getF(self.mu) if num_samples is not None: sample_shape = (num_samples,) + self.batch_shape else: sample_shape = self.batch_shape u = F.uniform(0, 1, shape=sample_shape) # Make sure that the generated samples are larger than condition_above. # This is easy to ensure when using inverse-survival sampling: we simply # multiply `u ~ Uniform(0, 1)` by `S(y)` to ensure that `x > y`. with autograd.pause(): if lower_bound is not None: survival = self.log_survival(lower_bound).exp() u = u * survival x = (self.mu + self.sigma * (F.log1p(-u) - F.log(u))).exp() return x
[docs]class LoglogisticOutput(TPPDistributionOutput): args_dim: Dict[str, int] = {"mu": 1, "sigma": 1} distr_cls: type = Loglogistic
[docs] @classmethod def domain_map(cls, F, mu, sigma): r""" Maps raw tensors to valid arguments for constructing a log-logistic distribution. Parameters ---------- F MXNet backend. mu Mean of the underlying logistic distribution. Shape `(*batch_shape, 1)` sigma Scale of the underlying logistic distribution. Shape `(*batch_shape, 1)` Returns ------- Tuple[Tensor, Tensor] Two squeezed tensors of shape `(*batch_shape)`. The sigma parameter is strictly positive. """ sigma = F.Activation(sigma, "softrelu") return mu.squeeze(axis=-1), sigma.squeeze(axis=-1)
@property def event_shape(self) -> Tuple: return ()