# Copyright 2020 Huawei Technologies Co., Ltd
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
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# http://www.apache.org/licenses/LICENSE-2.0
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# ============================================================================
"""Beta Distribution"""
import numpy as np
from mindspore.ops import operations as P
from mindspore.ops import functional as F
from mindspore.ops import composite as C
import mindspore.nn as nn
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
from .distribution import Distribution
from ._utils.utils import check_greater_zero, check_distribution_name
from ._utils.custom_ops import log_generic
[文档]class Beta(Distribution):
r"""
Beta distribution.
A Beta distributio is a continuous distribution with the range :math:`[0, 1]` and the probability density function:
.. math::
f(x, \alpha, \beta) = x^\alpha (1-x)^{\beta - 1} / B(\alpha, \beta),
where :math:`B` is the Beta function.
Args:
concentration1 (int, float, list, numpy.ndarray, Tensor): The concentration1,
also know as alpha of the Beta distribution. Default: ``None`` .
concentration0 (int, float, list, numpy.ndarray, Tensor): The concentration0, also know as
beta of the Beta distribution. Default: ``None`` .
seed (int): The seed used in sampling. The global seed is used if it is None. Default: ``None`` .
dtype (mindspore.dtype): The type of the event samples. Default: ``mstype.float32`` .
name (str): The name of the distribution. Default: ``'Beta'`` .
Note:
- `concentration1` and `concentration0` must be greater than zero.
- `dist_spec_args` are `concentration1` and `concentration0`.
- `dtype` must be a float type because Beta distributions are continuous.
Raises:
ValueError: When concentration1 <= 0 or concentration0 >=1.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``Ascend``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Beta distribution of the concentration1 3.0 and the concentration0 4.0.
>>> b1 = msd.Beta([3.0], [4.0], dtype=mindspore.float32)
>>> # A Beta distribution can be initialized without arguments.
>>> # In this case, `concentration1` and `concentration0` must be passed in through arguments.
>>> b2 = msd.Beta(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([0.1, 0.5, 0.8], dtype=mindspore.float32)
>>> concentration1_a = Tensor([2.0], dtype=mindspore.float32)
>>> concentration0_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> concentration1_b = Tensor([1.0], dtype=mindspore.float32)
>>> concentration0_b = Tensor([1.0, 1.5, 2.0], dtype=mindspore.float32)
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob` and `log_prob`, have the same arguments as follows.
>>> # Args:
>>> # value (Tensor): the value to be evaluated.
>>> # concentration1 (Tensor): the concentration1 of the distribution. Default: self._concentration1.
>>> # concentration0 (Tensor): the concentration0 of the distribution. Default: self._concentration0.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function
>>> ans = b1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to the distribution b.
>>> ans = b1.prob(value, concentration1_b, concentration0_b)
>>> print(ans.shape)
(3,)
>>> # `concentration1` and `concentration0` must be passed in during function calls
>>> ans = b2.prob(value, concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `sd`, `mode`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> # concentration1 (Tensor): the concentration1 of the distribution. Default: self._concentration1.
>>> # concentration0 (Tensor): the concentration0 of the distribution. Default: self._concentration0.
>>> # Example of `mean`, `sd`, `mode`, `var`, and `entropy` are similar.
>>> ans = b1.mean()
>>> print(ans.shape)
(1,)
>>> ans = b1.mean(concentration1_b, concentration0_b)
>>> print(ans.shape)
(3,)
>>> # `concentration1` and `concentration0` must be passed in during function calls.
>>> ans = b2.mean(concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
>>> # Args:
>>> # dist (str): the type of the distributions. Only "Beta" is supported.
>>> # concentration1_b (Tensor): the concentration1 of distribution b.
>>> # concentration0_b (Tensor): the concentration0 of distribution b.
>>> # concentration1_a (Tensor): the concentration1 of distribution a.
>>> # Default: self._concentration1.
>>> # concentration0_a (Tensor): the concentration0 of distribution a.
>>> # Default: self._concentration0.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = b1.kl_loss('Beta', concentration1_b, concentration0_b)
>>> print(ans.shape)
(3,)
>>> ans = b1.kl_loss('Beta', concentration1_b, concentration0_b, concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Additional `concentration1` and `concentration0` must be passed in.
>>> ans = b2.kl_loss('Beta', concentration1_b, concentration0_b, concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> # shape (tuple): the shape of the sample. Default: ()
>>> # concentration1 (Tensor): the concentration1 of the distribution. Default: self._concentration1.
>>> # concentration0 (Tensor): the concentration0 of the distribution. Default: self._concentration0.
>>> ans = b1.sample()
>>> print(ans.shape)
(1,)
>>> ans = b1.sample((2,3))
>>> print(ans.shape)
(2, 3, 1)
>>> ans = b1.sample((2,3), concentration1_b, concentration0_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = b2.sample((2,3), concentration1_a, concentration0_a)
>>> print(ans.shape)
(2, 3, 3)
"""
def __init__(self,
concentration1=None,
concentration0=None,
seed=None,
dtype=mstype.float32,
name="Beta"):
"""
Constructor of Beta.
"""
param = dict(locals())
param['param_dict'] = {
'concentration1': concentration1, 'concentration0': concentration0}
valid_dtype = mstype.float_type
Validator.check_type_name(
"dtype", dtype, valid_dtype, type(self).__name__)
# As some operators can't accept scalar input, check the type here
if isinstance(concentration0, float):
raise TypeError("Input concentration0 can't be scalar")
if isinstance(concentration1, float):
raise TypeError("Input concentration1 can't be scalar")
super(Beta, self).__init__(seed, dtype, name, param)
self._concentration1 = self._add_parameter(
concentration1, 'concentration1')
self._concentration0 = self._add_parameter(
concentration0, 'concentration0')
if self._concentration1 is not None:
check_greater_zero(self._concentration1, "concentration1")
if self._concentration0 is not None:
check_greater_zero(self._concentration0, "concentration0")
# ops needed for the class
self.log = log_generic
self.log1p = P.Log1p()
self.neg = P.Neg()
self.pow = P.Pow()
self.squeeze = P.Squeeze(0)
self.cast = P.Cast()
self.shape = P.Shape()
self.select = P.Select()
self.logicaland = P.LogicalAnd()
self.greater = P.Greater()
self.digamma = nn.DiGamma()
self.lbeta = nn.LBeta()
def extend_repr(self):
"""Display instance object as string."""
if self.is_scalar_batch:
s = 'concentration1 = {}, concentration0 = {}'.format(
self._concentration1, self._concentration0)
else:
s = 'batch_shape = {}'.format(self._broadcast_shape)
return s
@property
def concentration1(self):
"""
Return the concentration1, also know as the alpha of the Beta distribution,
after casting to dtype.
Output:
Tensor, the concentration1 parameter of the distribution.
"""
return self._concentration1
@property
def concentration0(self):
"""
Return the concentration0, also know as the beta of the Beta distribution,
after casting to dtype.
Output:
Tensor, the concentration2 parameter of the distribution.
"""
return self._concentration0
def _get_dist_type(self):
return "Beta"
def _get_dist_args(self, concentration1=None, concentration0=None):
if concentration1 is not None:
self.checktensor(concentration1, 'concentration1')
else:
concentration1 = self._concentration1
if concentration0 is not None:
self.checktensor(concentration0, 'concentration0')
else:
concentration0 = self._concentration0
return concentration1, concentration0
def _mean(self, concentration1=None, concentration0=None):
"""
The mean of the distribution.
"""
concentration1, concentration0 = self._check_param_type(
concentration1, concentration0)
return concentration1 / (concentration1 + concentration0)
def _var(self, concentration1=None, concentration0=None):
"""
The variance of the distribution.
"""
concentration1, concentration0 = self._check_param_type(
concentration1, concentration0)
total_concentration = concentration1 + concentration0
return concentration1 * concentration0 / (self.pow(total_concentration, 2) * (total_concentration + 1.))
def _mode(self, concentration1=None, concentration0=None):
"""
The mode of the distribution.
"""
concentration1, concentration0 = self._check_param_type(
concentration1, concentration0)
comp1 = self.greater(concentration1, 1.)
comp2 = self.greater(concentration0, 1.)
cond = self.logicaland(comp1, comp2)
batch_shape = self.shape(concentration1 + concentration0)
nan = F.fill(self.dtype, batch_shape, np.nan)
mode = (concentration1 - 1.) / (concentration1 + concentration0 - 2.)
return self.select(cond, mode, nan)
def _entropy(self, concentration1=None, concentration0=None):
r"""
Evaluate entropy.
.. math::
H(X) = \log(\Beta(\alpha, \beta)) - (\alpha - 1) * \digamma(\alpha)
- (\beta - 1) * \digamma(\beta) + (\alpha + \beta - 2) * \digamma(\alpha + \beta)
"""
concentration1, concentration0 = self._check_param_type(
concentration1, concentration0)
total_concentration = concentration1 + concentration0
return self.lbeta(concentration1, concentration0) \
- (concentration1 - 1.) * self.digamma(concentration1) \
- (concentration0 - 1.) * self.digamma(concentration0) \
+ (total_concentration - 2.) * self.digamma(total_concentration)
def _cross_entropy(self, dist, concentration1_b, concentration0_b, concentration1_a=None, concentration0_a=None):
r"""
Evaluate cross entropy between Beta distributions.
Args:
dist (str): Type of the distributions. Should be "Beta" in this case.
concentration1_b (Tensor): concentration1 of distribution b.
concentration0_b (Tensor): concentration0 of distribution b.
concentration1_a (Tensor): concentration1 of distribution a. Default: self._concentration1.
concentration0_a (Tensor): concentration0 of distribution a. Default: self._concentration0.
"""
check_distribution_name(dist, 'Beta')
return self._entropy(concentration1_a, concentration0_a) \
+ self._kl_loss(dist, concentration1_b, concentration0_b,
concentration1_a, concentration0_a)
def _log_prob(self, value, concentration1=None, concentration0=None):
r"""
Evaluate log probability.
Args:
value (Tensor): The value to be evaluated.
concentration1 (Tensor): The concentration1 of the distribution. Default: self._concentration1.
concentration0 (Tensor): The concentration0 the distribution. Default: self._concentration0.
.. math::
L(x) = (\alpha - 1) * \log(x) + (\beta - 1) * \log(1 - x) - \log(\Beta(\alpha, \beta))
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
concentration1, concentration0 = self._check_param_type(
concentration1, concentration0)
log_unnormalized_prob = (concentration1 - 1.) * self.log(value) \
+ (concentration0 - 1.) * self.log1p(self.neg(value))
return log_unnormalized_prob - self.lbeta(concentration1, concentration0)
def _kl_loss(self, dist, concentration1_b, concentration0_b, concentration1_a=None, concentration0_a=None):
r"""
Evaluate Beta-Beta KL divergence, i.e. KL(a||b).
Args:
dist (str): The type of the distributions. Should be "Beta" in this case.
concentration1_b (Tensor): The concentration1 of distribution b.
concentration0_b (Tensor): The concentration0 distribution b.
concentration1_a (Tensor): The concentration1 of distribution a. Default: self._concentration1.
concentration0_a (Tensor): The concentration0 distribution a. Default: self._concentration0.
.. math::
KL(a||b) = \log(\Beta(\alpha_{b}, \beta_{b})) - \log(\Beta(\alpha_{a}, \beta_{a}))
- \digamma(\alpha_{a}) * (\alpha_{b} - \alpha_{a})
- \digamma(\beta_{a}) * (\beta_{b} - \beta_{a})
+ \digamma(\alpha_{a} + \beta_{a}) * (\alpha_{b} + \beta_{b} - \alpha_{a} - \beta_{a})
"""
check_distribution_name(dist, 'Beta')
concentration1_b = self._check_value(
concentration1_b, 'concentration1_b')
concentration0_b = self._check_value(
concentration0_b, 'concentration0_b')
concentration1_b = self.cast(concentration1_b, self.parameter_type)
concentration0_b = self.cast(concentration0_b, self.parameter_type)
concentration1_a, concentration0_a = self._check_param_type(
concentration1_a, concentration0_a)
total_concentration_a = concentration1_a + concentration0_a
total_concentration_b = concentration1_b + concentration0_b
log_normalization_a = self.lbeta(concentration1_a, concentration0_a)
log_normalization_b = self.lbeta(concentration1_b, concentration0_b)
return (log_normalization_b - log_normalization_a) \
- (self.digamma(concentration1_a) * (concentration1_b - concentration1_a)) \
- (self.digamma(concentration0_a) * (concentration0_b - concentration0_a)) \
+ (self.digamma(total_concentration_a) *
(total_concentration_b - total_concentration_a))
def _sample(self, shape=(), concentration1=None, concentration0=None):
"""
Sampling.
Args:
shape (tuple): The shape of the sample. Default: ().
concentration1 (Tensor): The concentration1 of the samples. Default: self._concentration1.
concentration0 (Tensor): The concentration0 of the samples. Default: self._concentration0.
Returns:
Tensor, with the shape being shape + batch_shape.
"""
shape = self.checktuple(shape, 'shape')
concentration1, concentration0 = self._check_param_type(
concentration1, concentration0)
batch_shape = self.shape(concentration1 + concentration0)
origin_shape = shape + batch_shape
if origin_shape == ():
sample_shape = (1,)
else:
sample_shape = origin_shape
ones = F.fill(self.dtype, sample_shape, 1.0)
sample_gamma1 = C.gamma(
sample_shape, alpha=concentration1, beta=ones, seed=self.seed)
sample_gamma2 = C.gamma(
sample_shape, alpha=concentration0, beta=ones, seed=self.seed)
sample_beta = sample_gamma1 / (sample_gamma1 + sample_gamma2)
value = self.cast(sample_beta, self.dtype)
if origin_shape == ():
value = self.squeeze(value)
return value