Source code for mindspore.nn.probability.distribution.transformed_distribution
# Copyright 2020 Huawei Technologies Co., Ltd
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# ============================================================================
"""Transformed Distribution"""
import numpy as np
from mindspore import _checkparam as validator
from mindspore.ops import operations as P
from mindspore.common import dtype as mstype
import mindspore.nn as nn
from .distribution import Distribution
from ._utils.utils import raise_not_impl_error
from ._utils.custom_ops import exp_generic, log_generic
[docs]class TransformedDistribution(Distribution):
"""
Transformed Distribution.
This class contains a bijector and a distribution and transforms the original distribution
to a new distribution through the operation defined by the bijector.
If :math:`X` is an random variable following the underying distribution,
and :math:`g(x)` is a function represented by the bijector,
then :math:`Y = g(X)` is a random variable following the transformed distribution.
Args:
bijector (Bijector): The transformation to perform.
distribution (Distribution): The original distribution. Must be a float dtype.
seed (int): The seed is used in sampling. The global seed is used if it is None. Default: None.
If this seed is given when a TransformedDistribution object is initialized, the object's sampling function
will use this seed; elsewise, the underlying distribution's seed will be used.
name (str): The name of the transformed distribution. Default: 'transformed_distribution'.
Note:
The arguments used to initialize the original distribution cannot be None.
For example, mynormal = msd.Normal(dtype=mindspore.float32) cannot be used to initialized a
TransformedDistribution since `mean` and `sd` are not specified.
`batch_shape` is the batch_shape of the original distribution.
`broadcast_shape` is the broadcast shape between the original distribution and bijector.
`is_scalar_batch` is only true if both the original distribution and the bijector are scalar batches.
`default_parameters`, `parameter_names` and `parameter_type` are set to be consistent with the original
distribution. Derived class can overwrite `default_parameters` and `parameter_names` by calling
`reset_parameters` followed by `add_parameter`.
Raises:
TypeError: When the input `bijector` is not a Bijector instance.
TypeError: When the input `distribution` is not a Distribution instance.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> import numpy as np
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> import mindspore.nn.probability.bijector as msb
>>> from mindspore import Tensor
>>> class Net(nn.Cell):
... def __init__(self, shape, dtype=mindspore.float32, seed=0, name='transformed_distribution'):
... super(Net, self).__init__()
... # create TransformedDistribution distribution
... self.exp = msb.Exp()
... self.normal = msd.Normal(0.0, 1.0, dtype=dtype)
... self.lognormal = msd.TransformedDistribution(self.exp, self.normal, seed=seed, name=name)
... self.shape = shape
...
... def construct(self, value):
... cdf = self.lognormal.cdf(value)
... sample = self.lognormal.sample(self.shape)
... return cdf, sample
>>> shape = (2, 3)
>>> net = Net(shape=shape, name="LogNormal")
>>> x = np.array([2.0, 3.0, 4.0, 5.0]).astype(np.float32)
>>> tx = Tensor(x, dtype=mindspore.float32)
>>> cdf, sample = net(tx)
>>> print(sample.shape)
(2, 3)
"""
def __init__(self,
bijector,
distribution,
seed=None,
name="transformed_distribution"):
"""
Constructor of transformed_distribution class.
"""
param = dict(locals())
validator.check_value_type('bijector', bijector,
[nn.probability.bijector.Bijector], type(self).__name__)
validator.check_value_type('distribution', distribution,
[Distribution], type(self).__name__)
validator.check_type_name(
"dtype", distribution.dtype, mstype.float_type, type(self).__name__)
super(TransformedDistribution, self).__init__(
seed, distribution.dtype, name, param)
self._bijector = bijector
self._distribution = distribution
# set attributes
self._is_linear_transformation = self.bijector.is_constant_jacobian
self._dtype = self.distribution.dtype
self._is_scalar_batch = self.distribution.is_scalar_batch and self.bijector.is_scalar_batch
self._batch_shape = self.distribution.batch_shape
self.default_parameters = self.distribution.default_parameters
self.parameter_names = self.distribution.parameter_names
# by default, set the parameter_type to be the distribution's parameter_type
self.parameter_type = self.distribution.parameter_type
self.exp = exp_generic
self.log = log_generic
self.isnan = P.IsNan()
self.cast_base = P.Cast()
self.equal_base = P.Equal()
self.select_base = P.Select()
self.fill_base = P.Fill()
# broadcast bijector batch_shape and distribution batch_shape
self._broadcast_shape = self._broadcast_bijector_dist()
@property
def bijector(self):
"""
Return the bijector of the transformed distribution.
Output:
Bijector, the bijector of the transformed distribution.
"""
return self._bijector
@property
def distribution(self):
"""
Return the underlying distribution of the transformed distribution.
Output:
Bijector, the underlying distribution of the transformed distribution.
"""
return self._distribution
@property
def dtype(self):
"""
Return the dtype of the transformed distribution.
Output:
Mindspore.dtype, the dtype of the transformed distribution.
"""
return self._dtype
@property
def is_linear_transformation(self):
"""
Return whether the transformation is linear.
Output:
Bool, true if the transformation is linear, and false otherwise.
"""
return self._is_linear_transformation
def _broadcast_bijector_dist(self):
"""
check if the batch shape of base distribution and the bijector is broadcastable.
"""
if self.batch_shape is None or self.bijector.batch_shape is None:
return None
bijector_shape_tensor = self.fill_base(
self.dtype, self.bijector.batch_shape, 0.0)
dist_shape_tensor = self.fill_base(self.dtype, self.batch_shape, 0.0)
return (bijector_shape_tensor + dist_shape_tensor).shape
def _cdf(self, value, *args, **kwargs):
r"""
.. math::
Y = g(X)
P(Y <= a) = P(X <= g^{-1}(a))
"""
inverse_value = self.bijector("inverse", value)
return self.distribution("cdf", inverse_value, *args, **kwargs)
def _log_cdf(self, value, *args, **kwargs):
return self.log(self._cdf(value, *args, **kwargs))
def _survival_function(self, value, *args, **kwargs):
return 1.0 - self._cdf(value, *args, **kwargs)
def _log_survival(self, value, *args, **kwargs):
return self.log(self._survival_function(value, *args, **kwargs))
def _log_prob(self, value, *args, **kwargs):
r"""
.. math::
Y = g(X)
Py(a) = Px(g^{-1}(a)) * (g^{-1})'(a)
\log(Py(a)) = \log(Px(g^{-1}(a))) + \log((g^{-1})'(a))
"""
inverse_value = self.bijector("inverse", value)
unadjust_prob = self.distribution(
"log_prob", inverse_value, *args, **kwargs)
log_jacobian = self.bijector("inverse_log_jacobian", value)
isneginf = self.equal_base(unadjust_prob, -np.inf)
isnan = self.equal_base(unadjust_prob + log_jacobian, np.nan)
return self.select_base(isneginf,
self.select_base(
isnan, unadjust_prob + log_jacobian, unadjust_prob),
unadjust_prob + log_jacobian)
def _prob(self, value, *args, **kwargs):
return self.exp(self._log_prob(value, *args, **kwargs))
def _sample(self, *args, **kwargs):
org_sample = self.distribution("sample", *args, **kwargs)
return self.bijector("forward", org_sample)
def _mean(self, *args, **kwargs):
"""
Note:
This function maybe overridden by derived class.
"""
if not self.is_linear_transformation:
raise_not_impl_error("mean")
return self.bijector("forward", self.distribution("mean", *args, **kwargs))