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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
# express or implied. See the License for the specific language governing
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from typing import List, Optional, Tuple, Type
import numpy as np
from gluonts.core.component import validated
from gluonts.mx import Tensor
from gluonts.mx.util import make_nd_diag
from .distribution import Distribution, _sample_multiple, getF
from .distribution_output import DistributionOutput
[docs]class Dirichlet(Distribution):
r"""
Dirichlet distribution, specified by the concentration vector alpha of
length d. https://en.wikipedia.org/wiki/Dirichlet_distribution.
The Dirichlet distribution is defined on the open (d-1)-simplex, which
means that a sample (or observation) x = (x_0,..., x_{d-1}) must satisfy:
sum_k x_k = 1 and for all k, x_k > 0.
Parameters
----------
alpha
concentration vector, of shape (..., d)
F
A module that can either refer to the Symbol API or the NDArray
API in MXNet
"""
is_reparameterizable = False
@validated()
def __init__(self, alpha: Tensor, float_type: Type = np.float32) -> None:
self.alpha = alpha
self.float_type = float_type
@property
def F(self):
return getF(self.alpha)
@property
def args(self) -> List:
return [self.alpha]
@property
def batch_shape(self) -> Tuple:
return self.alpha.shape[:-1]
@property
def event_shape(self) -> Tuple:
return self.alpha.shape[-1:]
@property
def event_dim(self) -> int:
return 1
[docs] def log_prob(self, x: Tensor) -> Tensor:
F = self.F
# Normalize observations in case of mean_scaling
sum_x = F.sum(x, axis=-1).expand_dims(axis=-1)
x = F.broadcast_div(x, sum_x)
alpha = self.alpha
sum_alpha = F.sum(alpha, axis=-1)
log_beta = F.sum(F.gammaln(alpha), axis=-1) - F.gammaln(sum_alpha)
l_x = F.sum((alpha - 1) * F.log(x), axis=-1)
ll = l_x - log_beta
return ll
@property
def mean(self) -> Tensor:
F = self.F
alpha = self.alpha
sum_alpha = F.sum(alpha, axis=-1)
return F.broadcast_div(alpha, sum_alpha.expand_dims(axis=-1))
@property
def variance(self) -> Tensor:
F = self.F
alpha = self.alpha
d = int(F.ones_like(self.alpha).sum(axis=-1).max().asscalar())
scale = F.sqrt(F.sum(alpha, axis=-1) + 1).expand_dims(axis=-1)
scaled_alpha = F.broadcast_div(self.mean, scale)
cross = F.linalg_gemm2(
scaled_alpha.expand_dims(axis=-1),
scaled_alpha.expand_dims(axis=-1),
transpose_b=True,
)
diagonal = make_nd_diag(F, F.broadcast_div(scaled_alpha, scale), d)
return diagonal - cross
[docs] def sample(
self, num_samples: Optional[int] = None, dtype=np.float32
) -> Tensor:
def s(alpha: Tensor) -> Tensor:
F = getF(alpha)
samples_gamma = F.sample_gamma(
alpha=alpha, beta=F.ones_like(alpha), dtype=dtype
)
sum_gamma = F.sum(samples_gamma, axis=-1, keepdims=True)
samples_s = F.broadcast_div(samples_gamma, sum_gamma)
return samples_s
samples = _sample_multiple(
s, alpha=self.alpha, num_samples=num_samples
)
return samples
[docs]class DirichletOutput(DistributionOutput):
@validated()
def __init__(self, dim: int) -> None:
super().__init__(self)
assert dim > 1, "Dimension should be larger than one."
self.args_dim = {"alpha": dim}
self.distr_cls = Dirichlet
self.dim = dim
self.mask = None
[docs] def distribution(self, distr_args, loc=None, scale=None) -> Distribution:
distr = Dirichlet(distr_args)
return distr
[docs] def domain_map(self, F, alpha_vector):
# apply softplus to the elements of alpha vector
alpha = F.Activation(alpha_vector, act_type="softrelu")
return alpha
@property
def event_shape(self) -> Tuple:
return (self.dim,)