mindspore.nn.probability.distribution.Gamma

class mindspore.nn.probability.distribution.Gamma(concentration=None, rate=None, seed=None, dtype=mstype.float32, name='Gamma')[source]

Gamma distribution. A Gamma distributio is a continuous distribution with the range \([0, 1]\) and the probability density function:

\[f(x, \alpha, \beta) = \beta^\alpha / \Gamma(\alpha) x^{\alpha - 1} \exp(-\beta x).\]

where \(G\) is the Gamma function, and \(\alpha, \beta\) are the concentration and the rate of the distribution respectively.

Parameters

concentration (int, float, list, numpy.ndarray, Tensor) – The concentration, also know as alpha of the Gamma distribution. Default: None.
rate (int, float, list, numpy.ndarray, Tensor) – The rate, also know as beta of the Gamma distribution. Default: None.
seed (int) – The seed used in sampling. The global seed is used if it is None. Default: None.
dtype (mindspore.dtype) – The type of the event samples. Default: mstype.float32.
name (str) – The name of the distribution. Default: ‘Gamma’.

Inputs and Outputs of APIs:

The accessible APIs of the Gamma distribution are defined in the base class, including:

prob, log_prob, cdf, log_cdf, survival_function, and log_survival
mean, sd, mode, var, and entropy
kl_loss and cross_entropy
sample

For more details of all APIs, including the inputs and outputs of all APIs of the Gamma distribution, please refer to mindspore.nn.probability.distribution.Distribution, and examples below.

Supported Platforms:

Ascend

Note

concentration and rate must be greater than zero. dist_spec_args are concentration and rate. dtype must be a float type because Gamma distributions are continuous.

Raises

ValueError – When concentration <= 0 or rate <= 0.
TypeError – When the input dtype is not a subclass of float.

Examples

>>> import mindspore
>>> import mindspore.nn as nn
>>> import mindspore.nn.probability.distribution as msd
>>> from mindspore import Tensor
>>> # To initialize a Gamma distribution of the concentration 3.0 and the rate 4.0.
>>> g1 = msd.Gamma([3.0], [4.0], dtype=mindspore.float32)
>>> # A Gamma distribution can be initialized without arguments.
>>> # In this case, `concentration` and `rate` must be passed in through arguments.
>>> g2 = msd.Gamma(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([1.0, 2.0, 3.0], dtype=mindspore.float32)
>>> concentration_a = Tensor([2.0], dtype=mindspore.float32)
>>> rate_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> concentration_b = Tensor([1.0], dtype=mindspore.float32)
>>> rate_b = Tensor([1.0, 1.5, 2.0], dtype=mindspore.float32)
>>>
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob`, `log_prob`, `cdf`, `log_cdf`, `survival_function`, and `log_survival`,
>>> # have the same arguments as follows.
>>> # Args:
>>> #     value (Tensor): the value to be evaluated.
>>> #     concentration (Tensor): the concentration of the distribution. Default: self._concentration.
>>> #     rate (Tensor): the rate of the distribution. Default: self._rate.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function
>>> ans = g1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to the distribution b.
>>> ans = g1.prob(value, concentration_b, rate_b)
>>> print(ans.shape)
(3,)
>>> # `concentration` and `rate` must be passed in during function calls for g2.
>>> ans = g2.prob(value, concentration_a, rate_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `sd`, `mode`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> #     concentration (Tensor): the concentration of the distribution. Default: self._concentration.
>>> #     rate (Tensor): the rate of the distribution. Default: self._rate.
>>> # Example of `mean`, `sd`, `mode`, `var`, and `entropy` are similar.
>>> ans = g1.mean()
>>> print(ans.shape)
(1,)
>>> ans = g1.mean(concentration_b, rate_b)
>>> print(ans.shape)
(3,)
>>> # `concentration` and `rate` must be passed in during function calls.
>>> ans = g2.mean(concentration_a, rate_a)
>>> print(ans.shape)
(3,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
>>> # Args:
>>> #     dist (str): the type of the distributions. Only "Gamma" is supported.
>>> #     concentration_b (Tensor): the concentration of distribution b.
>>> #     rate_b (Tensor): the rate of distribution b.
>>> #     concentration_a (Tensor): the concentration of distribution a. Default: self._concentration.
>>> #     rate_a (Tensor): the rate of distribution a. Default: self._rate.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = g1.kl_loss('Gamma', concentration_b, rate_b)
>>> print(ans.shape)
(3,)
>>> ans = g1.kl_loss('Gamma', concentration_b, rate_b, concentration_a, rate_a)
>>> print(ans.shape)
(3,)
>>> # Additional `concentration` and `rate` must be passed in.
>>> ans = g2.kl_loss('Gamma', concentration_b, rate_b, concentration_a, rate_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> #     shape (tuple): the shape of the sample. Default: ()
>>> #     concentration (Tensor): the concentration of the distribution. Default: self._concentration.
>>> #     rate (Tensor): the rate of the distribution. Default: self._rate.
>>> ans = g1.sample()
>>> print(ans.shape)
(1,)
>>> ans = g1.sample((2,3))
>>> print(ans.shape)
(2, 3, 1)
>>> ans = g1.sample((2,3), concentration_b, rate_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = g2.sample((2,3), concentration_a, rate_a)
>>> print(ans.shape)
(2, 3, 3)

property concentration

Return the concentration, also know as the alpha of the Gamma distribution, after casting to dtype.

Output:: Tensor, the concentration parameter of the distribution.

extend_repr()[source]: Display instance object as string.

property rate

Return the rate, also know as the beta of the Gamma distribution, after casting to dtype.

Output:: Tensor, the rate parameter of the distribution.