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"""Laplace Distribution"""
from __future__ import absolute_import
from __future__ import division
from mindspore.ops import operations as P
from mindspore import _checkparam as Validator
from mindspore.common import dtype as mstype
from mindspore.nn.probability.distribution import Distribution
from mindspore.nn.probability.distribution._utils.utils import check_greater_zero
[docs]class Laplace(Distribution):
r"""
Laplace distribution.
A Laplace distribution is a continuous distribution with the range :math:`(-\inf, \inf)`
and the probability density function:
.. math::
f(x, \mu, b) = 1 / (2 * b) * \exp(-abs(x - \mu) / b).
where :math:`\mu, b` are the mean and the scale of the laplace distribution respectively.
Args:
mean (Union[int, float, list, numpy.ndarray, Tensor], optional): The mean of the distribution.
If this arg is ``None`` , then the mean of the distribution will be passed in runtime. Default: ``None`` .
sd (Union[int, float, list, numpy.ndarray, Tensor], optional): The scale of the distribution.
If this arg is ``None`` , then the scale of the distribution will be passed in runtime. Default: ``None`` .
seed (int, optional): The seed used in sampling. The global seed is used if it is None. Default: ``None`` .
dtype (mindspore.dtype, optional): The type of the event samples. Default: ``mstype.float32`` .
name (str, optional): The name of the distribution. Default: ``'Laplace'`` .
Note:
- `sd` must be greater than zero.
- `dtype` must be a float type because Laplace distributions are continuous.
- If the arg `mean` or `sd` is passed in runtime, then it will be used as the parameter value.
Otherwise, the value passed in the constructor will be used.
Raises:
ValueError: When sd <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``Ascend`` ``GPU`` ``CPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> from mindspore.nn.probability.distribution import Laplace
>>> from mindspore import Tensor
>>> # To initialize a Laplace distribution of the mean 3.0 and the scale 4.0.
>>> n1 = Laplace(3.0, 4.0, dtype=mindspore.float32)
>>> # A Laplace distribution can be initialized without arguments.
>>> # In this case, `mean` and `sd` must be passed in through arguments.
>>> n2 = Laplace(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32)
>>> mean_a = Tensor([2.0], dtype=mindspore.float32)
>>> sd_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> mean_b = Tensor([1.0], dtype=mindspore.float32)
>>> sd_b = Tensor([1.0, 1.5, 2.0], dtype=mindspore.float32)
>>> ans = n1.log_prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to the distribution b.
>>> ans = n1.log_prob(value, mean_b, sd_b)
>>> print(ans.shape)
(3,)
>>> # `mean` and `sd` must be passed in during function calls
>>> ans = n2.log_prob(value, mean_a, sd_a)
>>> print(ans.shape)
(3,)
"""
def __init__(self,
mean=None,
sd=None,
seed=None,
dtype=mstype.float32,
name="Laplace"):
"""
Constructor of Laplace.
"""
param = dict(locals())
param['param_dict'] = {'mean': mean, 'sd': sd}
valid_dtype = mstype.float_type
Validator.check_type_name("dtype", dtype, valid_dtype, type(self).__name__)
super(Laplace, self).__init__(seed, dtype, name, param)
self._mean_value = self._add_parameter(mean, 'mean')
self._sd_value = self._add_parameter(sd, 'sd')
if self._sd_value is not None:
check_greater_zero(self._sd_value, "Standard deviation")
self.log = P.Log()
self.cast = P.Cast()
self.abs = P.Abs()
def _log_prob(self, value, mean=None, sd=None):
r"""
Evaluate log probability of the laplace distribution.
Args:
value (Tensor): The value to be evaluated.
mean (Tensor, optional): The mean of the distribution. Default: self._mean_value.
sd (Tensor, optional): The scale the distribution. Default: self._sd_value.
.. math::
L(x) = -1* \abs{\frac{x - \mu}{\sigma}} - \log(2. * \sigma))
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
mean, sd = self._check_param_type(mean, sd)
pdf = -1.0 * (self.abs((value - mean) / sd)) - self.log(2. * sd)
return pdf