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"""StudentT Distribution"""
from __future__ import absolute_import
from __future__ import division
import numpy as np
import mindspore.nn as nn
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 StudentT(Distribution):
r"""
StudentT distribution.
A StudentT distribution is a continuous distribution with the range :math:`(-\inf, \inf)`
and the probability density function:
.. math::
f(x, \nu, \mu, \sigma) = (1 + y^2 / \nu)^{(-0.5*(\nu + 1))} / Z
where :math:`y = (x - \mu)/ \sigma`,
:math:`Z = abs(\sigma) * \sqrt{(\nu * \pi)} * \Gamma(0.5 * \nu) / \Gamma(0.5 * (\nu + 1))`,
:math:`\nu, \mu, \sigma` are the degrees of freedom , mean and sd of the laplace distribution respectively.
Args:
df (Union[int, float, list, numpy.ndarray, Tensor], optional): The degrees of freedom.
If this arg is None, then the df of the distribution will be passed in runtime. Default: None.
mean (Union[int, float, list, numpy.ndarray, Tensor], optional): The mean of the distribution.
If this arg is None, then the df of the distribution will be passed in runtime. Default: None.
sd (Union[int, float, list, numpy.ndarray, Tensor], optional): The standard deviation of the distribution.
If this arg is None, then the sd 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: 'StudentT'.
Note:
- `df` must be greater than zero.
- `sd` must be greater than zero.
- `dtype` must be a float type because StudentT distributions are continuous.
- If the arg `df`, `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 df <= 0.
ValueError: When sd <= 0.
TypeError: When the input `dtype` is not a subclass of float.
Supported Platforms:
``CPU``
Examples:
>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a StudentT distribution of the df 2.0, the mean 3.0 and the standard deviation 4.0.
>>> n1 = msd.StudentT(2.0, 3.0, 4.0, dtype=mindspore.float32)
>>> # A StudentT distribution can be initialized without arguments.
>>> # In this case, `df`, `mean` and `sd` must be passed in through arguments.
>>> n2 = msd.StudentT(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32)
>>> df_a = Tensor([2.0], dtype=mindspore.float32)
>>> mean_a = Tensor([2.0], dtype=mindspore.float32)
>>> sd_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> df_b = Tensor([1.0], 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, df_b, mean_b, sd_b)
>>> print(ans.shape)
(3,)
>>> # `mean` and `sd` must be passed in during function calls
>>> ans = n2.log_prob(value, df_a, mean_a, sd_a)
>>> print(ans.shape)
(3,)
"""
def __init__(self,
df=None,
mean=None,
sd=None,
seed=None,
dtype=mstype.float32,
name="StudentT"):
"""
Constructor of StudentT.
"""
param = dict(locals())
param['param_dict'] = {'df': df, 'mean': mean, 'sd': sd}
valid_dtype = mstype.float_type
Validator.check_type_name("dtype", dtype, valid_dtype, type(self).__name__)
super(StudentT, self).__init__(seed, dtype, name, param)
self._df_value = self._add_parameter(df, 'df')
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")
if self._df_value is not None:
check_greater_zero(self._df_value, "Degrees of freedom")
self.log1p = P.Log1p()
self.log = P.Log()
self.cast = P.Cast()
self.abs = P.Abs()
self.half = 0.5
self.half_log_pi = 0.5 * np.log(np.pi)
self.lgamma = nn.LGamma()
def _log_prob(self, value, df=None, mean=None, sd=None):
r"""
Evaluate log probability of the value of the StudentT distribution.
Args:
value (Tensor): The value to be evaluated.
df (Tensor, optional): The degrees of freedom of the distribution. Default: self._df_value.
mean (Tensor, optional): The mean of the distribution. Default: self._mean_value.
sd (Tensor, optional): The standard deviation the distribution. Default: self._sd_value.
.. math::
L(x) = -0.5 * (\nu + 1.) * \log((x - \mu) / \sigma + 1.)) + \log(\sqrt(\pi * \mu * \sigma^2))
+ log(\Gamma(\nu / 2.)) - log(\Gamma((\nu + 1.) / 2.))
"""
value = self._check_value(value, 'value')
value = self.cast(value, self.dtype)
df, mean, sd = self._check_param_type(df, mean, sd)
y = (value - mean) / sd
log_unnormalized_prob = -0.5 * (df + 1.) * self.log1p(y**2. / df)
log_normalization = self.log(self.abs(sd)) + 0.5 * self.log(df) + self.half_log_pi + \
self.lgamma(self.half * df) - self.lgamma(self.half * (df + 1.))
return log_unnormalized_prob - log_normalization