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

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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.
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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
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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 Weibull(TPPDistribution): r""" Weibull distribution. We use the parametrization of the Weibull distribution using the rate parameter :math:`b > 0` and the shape parameter :math:`k > 0`. The PDF is :math:`p(x) = b * k * x^{(k - 1)} * \exp(-b * x^k)`. An alternative parametrization is often used (e.g. on Wikipedia), where we use the scale parameter :math:`\lambda > 0` and the shape parameter :math:`k > 0`, and :math:`\lambda = b^{-1/k}`. """ is_reparametrizable = True @validated() def __init__(self, rate: Tensor, shape: Tensor) -> None: self.rate = rate self.shape = shape @property def batch_shape(self) -> Tuple: return self.rate.shape @property def event_shape(self) -> Tuple: return () @property def event_dim(self) -> int: return 0 @property def mean(self) -> Tensor: return nd.power(self.rate, -1.0 / self.shape) * nd.gamma( 1.0 + 1.0 / self.shape )
[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)`. The intensity of the Weibull distribution is :math:`\lambda(x) = b * k * x^{k - 1}`. """ log_x = x.clip(1e-10, np.inf).log() return self.rate.log() + self.shape.log() + (self.shape - 1) * log_x
[docs] def log_survival(self, x: Tensor) -> Tensor: r""" Logarithm of the survival function :math:`\log S(x) = \log(1 - CDF(x))`. The survival function of the Weibull distribution is :math:`S(x) = \exp(-b * x^k)`. """ # We need to add eps=1e-10 to avoid numerical instability of pow() return -self.rate * (x + 1e-10) ** self.shape
[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.rate) 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 = (-u.log() / self.rate) ** (1.0 / self.shape) return x
[docs]class WeibullOutput(TPPDistributionOutput): args_dim: Dict[str, int] = {"rate": 1, "shape": 1} distr_cls: type = Weibull
[docs] @classmethod def domain_map(cls, F, rate, shape): r""" Maps raw tensors to valid arguments for constructing a Weibull distribution. Parameters ---------- F MXNet backend. rate Rate (inverse scale) parameter of the Weibull distribution. Shape `(*batch_shape, 1)` shape Shape parameter of the Weibull distribution. Shape `(*batch_shape, 1)` Returns ------- Tuple[Tensor, Tensor] Two squeezed tensors of shape `(*batch_shape)`. Both tensors are strictly positive. """ rate = F.Activation(rate, "softrelu") shape = F.Activation(shape, "softrelu") return rate.squeeze(axis=-1), shape.squeeze(axis=-1)
@property def event_shape(self) -> Tuple: return ()