mindspore.nn.probability.distribution.StudentT

class mindspore.nn.probability.distribution.StudentT(df=None, mean=None, sd=None, seed=None, dtype=mstype.float32, name='StudentT')[source]

StudentT distribution. A StudentT distribution is a continuous distribution with the range \((-\inf, \inf)\) and the probability density function:

\[f(x, \nu, \mu, \sigma) = (1 + y^2 / \nu)^{(-0.5*(\nu + 1))} / Z\]

where \(y = (x - \mu)/ \sigma\), \(Z = abs(\sigma) * \sqrt{(\nu * \pi)} * \Gamma(0.5 * \nu) / \Gamma(0.5 * (\nu + 1))\), \(\nu, \mu, \sigma\) are the degrees of freedom , mean and sd of the laplace distribution respectively.

Parameters

  • 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
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,)
log_prob(value, df=None, mean=None, sd=None)

Evaluate log probability of the value of the StudentT distribution.

Parameters

  • value (Tensor) - the value to compute.

  • df (Tensor, optional) - the degrees of freedom of the distribution. Default: None .

  • mean (Tensor, optional) - the mean of the distribution. Default: None .

  • sd (Tensor, optional) - the standard deviation of the distribution. Default: None .

Returns

Tensor, the log value of the probability.