mindspore.nn.probability.distribution.StudentT

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

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:

• 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,)

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.