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’.

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, aka the alpha parameter, of the distribution.

Returns

Tensor, concentration.

property rate

Return the rate, aka the beta parameter, of the distribution.

Returns

Tensor, rate.

cdf(value, concentration, rate)

Compute the cumulatuve distribution function(CDF) of the given value.

Parameters

value (Tensor) - the value to compute.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the cumulatuve distribution function for the given input.

cross_entropy(dist, concentration_b, rate_b, concentration, rate)

Compute the cross entropy of two distribution

Parameters

dist (str) - the type of the other distribution.
concentration_b (Tensor) - the alpha parameter of the other distribution.
rate_b (Tensor) - the beta parameter of the other distribution.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the cross entropy.

entropy(concentration, rate)

Compute the value of the entropy.

Parameters

concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the entropy.

kl_loss(dist, concentration_b, rate_b, concentration, rate)

Compute the value of the K-L loss between two distribution, namely KL(a||b).

Parameters

dist (str) - the type of the other distribution.
concentration_b (Tensor) - the alpha parameter of the other distribution.
rate_b (Tensor) - the beta parameter of the other distribution.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

log_cdf(value, concentration, rate)

Compute the log value of the cumulatuve distribution function.

Parameters

value (Tensor) - the value to compute.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the log value of the cumulatuve distribution function.

log_prob(value, concentration, rate)

the log value of the probability.

Parameters

value (Tensor) - the value to compute.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the log value of the probability.

log_survival(value, concentration, rate)

Compute the log value of the survival function.

Parameters

value (Tensor) - the value to compute.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

mean(concentration, rate)

Compute the mean value of the distribution.

Parameters

concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the mean of the distribution.

mode(concentration, rate)

Compute the mode value of the distribution.

Parameters

concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the mode of the distribution.

prob(value, concentration, rate)

The probability of the given value. For the continuous distribution, it is the probability density function.

Parameters

value (Tensor) - the value to compute.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the probability.

sample(shape, concentration, rate)

Generate samples.

Parameters

shape (tuple) - the shape of the sample.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the sample following the distribution.

sd(concentration, rate)

The standard deviation.

Parameters

concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the standard deviation of the distribution.

survival_function(value, concentration, rate)

Compute the value of the survival function.

Parameters

value (Tensor) - the value to compute.
concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the value of the survival function.

var(concentration, rate)

Compute the variance of the distribution.

Parameters

concentration (Tensor) - the alpha parameter of the distribution. Default value: None.
rate (Tensor) - the beta parameter of the distribution. Default value: None.

Returns

Tensor, the variance of the distribution.