# 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, Tuple
from gluonts.core.component import validated
from gluonts.mx import Tensor
from .beta import Beta
from .deterministic import Deterministic
from .distribution import getF, softplus
from .distribution_output import DistributionOutput
from .mixture import MixtureDistribution
[docs]class ZeroAndOneInflatedBeta(MixtureDistribution):
r"""
Zero And One Inflated Beta distribution as in Raydonal Ospina, Silvia L.P.
Ferrari: Inflated Beta Distributions
Parameters
----------
alpha
Tensor containing the alpha shape parameters, of shape
`(*batch_shape, *event_shape)`.
beta
Tensor containing the beta shape parameters, of shape
`(*batch_shape, *event_shape)`.
zero_probability
Tensor containing the probability of zeros, of shape
`(*batch_shape, *event_shape)`.
one_probability
Tensor containing the probability of ones, of shape
`(*batch_shape, *event_shape)`.
F
"""
is_reparameterizable = False
@validated()
def __init__(
self,
alpha: Tensor,
beta: Tensor,
zero_probability: Tensor,
one_probability: Tensor,
) -> None:
F = getF(alpha)
self.alpha = alpha
self.beta = beta
self.zero_probability = zero_probability
self.one_probability = one_probability
self.beta_probability = 1 - zero_probability - one_probability
self.beta_distribution = Beta(alpha=alpha, beta=beta)
mixture_probs = F.stack(
zero_probability, one_probability, self.beta_probability, axis=-1
)
super().__init__(
components=[
Deterministic(alpha.zeros_like()),
Deterministic(alpha.ones_like()),
self.beta_distribution,
],
mixture_probs=mixture_probs,
)
[docs] def log_prob(self, x: Tensor) -> Tensor:
F = self.F
# mask zeros for the Beta distribution input to prevent NaN gradients
inputs = F.where(
F.broadcast_logical_or(x == 0, x == 1), x.zeros_like() + 0.5, x
)
# compute log density, case by case
return F.where(
x == 1,
F.log(self.one_probability.broadcast_like(x)),
F.where(
x == 0,
F.log(self.zero_probability.broadcast_like(x)),
F.log(self.beta_probability)
+ self.beta_distribution.log_prob(inputs),
),
)
[docs]class ZeroInflatedBeta(ZeroAndOneInflatedBeta):
r"""Zero Inflated Beta distribution as in Raydonal Ospina, Silvia L.P.
Ferrari: Inflated Beta Distributions.
Parameters
----------
alpha
Tensor containing the alpha shape parameters, of shape
`(*batch_shape, *event_shape)`.
beta
Tensor containing the beta shape parameters, of shape
`(*batch_shape, *event_shape)`.
zero_probability
Tensor containing the probability of zeros, of shape
`(*batch_shape, *event_shape)`.
F
"""
is_reparameterizable = False
@validated()
def __init__(
self, alpha: Tensor, beta: Tensor, zero_probability: Tensor
) -> None:
super().__init__(
alpha=alpha,
beta=beta,
zero_probability=zero_probability,
one_probability=alpha.zeros_like(),
)
[docs]class OneInflatedBeta(ZeroAndOneInflatedBeta):
r"""One Inflated Beta distribution as in Raydonal Ospina, Silvia L.P.
Ferrari: Inflated Beta Distributions.
Parameters
----------
alpha
Tensor containing the alpha shape parameters, of shape
`(*batch_shape, *event_shape)`.
beta
Tensor containing the beta shape parameters, of shape
`(*batch_shape, *event_shape)`.
one_probability
Tensor containing the probability of ones, of shape
`(*batch_shape, *event_shape)`.
F
"""
is_reparameterizable = False
@validated()
def __init__(
self, alpha: Tensor, beta: Tensor, one_probability: Tensor
) -> None:
super().__init__(
alpha=alpha,
beta=beta,
zero_probability=alpha.zeros_like(),
one_probability=one_probability,
)
[docs]class ZeroAndOneInflatedBetaOutput(DistributionOutput):
args_dim: Dict[str, int] = {
"alpha": 1,
"beta": 1,
"zero_probability": 1,
"one_probability": 1,
}
distr_cls: type = ZeroAndOneInflatedBeta
[docs] @classmethod
def domain_map(cls, F, alpha, beta, zero_probability, one_probability):
r"""
Maps raw tensors to valid arguments for constructing a
ZeroAndOneInflatedBeta distribution.
Parameters
----------
F:
alpha:
Tensor of shape `(*batch_shape, 1)`
beta:
Tensor of shape `(*batch_shape, 1)`
zero_probability:
Tensor of shape `(*batch_shape, 1)`
Returns
-------
Tuple[Tensor, Tensor, Tensor, Tensor]:
Four squeezed tensors, of shape `(*batch_shape)`: First two have
entries mapped to the positive orthant, zero_probability is mapped
to (0, 1), one_probability is mapped to (0, 1-zero_probability)
"""
alpha = F.maximum(softplus(F, alpha), cls.eps())
beta = F.maximum(softplus(F, beta), cls.eps())
zero_probability = F.sigmoid(zero_probability)
one_probability = (1 - zero_probability) * F.sigmoid(one_probability)
return (
alpha.squeeze(axis=-1),
beta.squeeze(axis=-1),
zero_probability.squeeze(axis=-1),
one_probability.squeeze(axis=-1),
)
@property
def event_shape(self) -> Tuple:
return ()
@property
def value_in_support(self) -> float:
return 0.5
[docs]class ZeroInflatedBetaOutput(ZeroAndOneInflatedBetaOutput):
args_dim: Dict[str, int] = {"alpha": 1, "beta": 1, "zero_probability": 1}
distr_cls: type = ZeroInflatedBeta
[docs] @classmethod
def domain_map(cls, F, alpha, beta, zero_probability):
r"""
Maps raw tensors to valid arguments for constructing a ZeroInflatedBeta
distribution.
Parameters
----------
F:
alpha:
Tensor of shape `(*batch_shape, 1)`
beta:
Tensor of shape `(*batch_shape, 1)`
zero_probability:
Tensor of shape `(*batch_shape, 1)`
Returns
-------
Tuple[Tensor, Tensor, Tensor]:
Three squeezed tensors, of shape `(*batch_shape)`: First two have
entries mapped to the positive orthant, last is mapped to (0,1)
"""
alpha = F.maximum(softplus(F, alpha), cls.eps())
beta = F.maximum(softplus(F, beta), cls.eps())
zero_probability = F.sigmoid(zero_probability)
return (
alpha.squeeze(axis=-1),
beta.squeeze(axis=-1),
zero_probability.squeeze(axis=-1),
)
[docs]class OneInflatedBetaOutput(ZeroInflatedBetaOutput):
args_dim: Dict[str, int] = {"alpha": 1, "beta": 1, "one_probability": 1}
distr_cls: type = OneInflatedBeta
[docs] @classmethod
def domain_map(cls, F, alpha, beta, one_probability):
return super().domain_map(F, alpha, beta, one_probability)