mindspore.nn.probability.distribution.Beta

class mindspore.nn.probability.distribution.Beta(concentration1=None, concentration0=None, seed=None, dtype=mstype.float32, name='Beta')[source]

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

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

where \(B\) is the Beta function.

Parameters

concentration1 (int, float, list, numpy.ndarray, Tensor) – The concentration1, also know as alpha of the Beta distribution. Default: None.
concentration0 (int, float, list, numpy.ndarray, Tensor) – The concentration0, also know as beta of the Beta 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: ‘Beta’.

Inputs and Outputs of APIs:

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

prob and log_prob
mean, sd, var, and entropy
kl_loss and cross_entropy
sample

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

Supported Platforms:

Ascend

Note

concentration1 and concentration0 must be greater than zero. dist_spec_args are concentration1 and concentration0. dtype must be a float type because Beta distributions are continuous.

Raises

ValueError – When concentration1 <= 0 or concentration0 >=1.
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 Beta distribution of the concentration1 3.0 and the concentration0 4.0.
>>> b1 = msd.Beta([3.0], [4.0], dtype=mindspore.float32)
>>> # A Beta distribution can be initialized without arguments.
>>> # In this case, `concentration1` and `concentration0` must be passed in through arguments.
>>> b2 = msd.Beta(dtype=mindspore.float32)
>>> # Here are some tensors used below for testing
>>> value = Tensor([0.1, 0.5, 0.8], dtype=mindspore.float32)
>>> concentration1_a = Tensor([2.0], dtype=mindspore.float32)
>>> concentration0_a = Tensor([2.0, 2.0, 2.0], dtype=mindspore.float32)
>>> concentration1_b = Tensor([1.0], dtype=mindspore.float32)
>>> concentration0_b = Tensor([1.0, 1.5, 2.0], dtype=mindspore.float32)
>>> # Private interfaces of probability functions corresponding to public interfaces, including
>>> # `prob` and `log_prob`, have the same arguments as follows.
>>> # Args:
>>> #     value (Tensor): the value to be evaluated.
>>> #     concentration1 (Tensor): the concentration1 of the distribution. Default: self._concentration1.
>>> #     concentration0 (Tensor): the concentration0 of the distribution. Default: self._concentration0.
>>> # Examples of `prob`.
>>> # Similar calls can be made to other probability functions
>>> # by replacing 'prob' by the name of the function
>>> ans = b1.prob(value)
>>> print(ans.shape)
(3,)
>>> # Evaluate with respect to the distribution b.
>>> ans = b1.prob(value, concentration1_b, concentration0_b)
>>> print(ans.shape)
(3,)
>>> # `concentration1` and `concentration0` must be passed in during function calls
>>> ans = b2.prob(value, concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Functions `mean`, `sd`, `mode`, `var`, and `entropy` have the same arguments.
>>> # Args:
>>> #     concentration1 (Tensor): the concentration1 of the distribution. Default: self._concentration1.
>>> #     concentration0 (Tensor): the concentration0 of the distribution. Default: self._concentration0.
>>> # Example of `mean`, `sd`, `mode`, `var`, and `entropy` are similar.
>>> ans = b1.mean()
>>> print(ans.shape)
(1,)
>>> ans = b1.mean(concentration1_b, concentration0_b)
>>> print(ans.shape)
(3,)
>>> # `concentration1` and `concentration0` must be passed in during function calls.
>>> ans = b2.mean(concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Interfaces of 'kl_loss' and 'cross_entropy' are the same:
>>> # Args:
>>> #     dist (str): the type of the distributions. Only "Beta" is supported.
>>> #     concentration1_b (Tensor): the concentration1 of distribution b.
>>> #     concentration0_b (Tensor): the concentration0 of distribution b.
>>> #     concentration1_a (Tensor): the concentration1 of distribution a.
>>> #       Default: self._concentration1.
>>> #     concentration0_a (Tensor): the concentration0 of distribution a.
>>> #       Default: self._concentration0.
>>> # Examples of `kl_loss`. `cross_entropy` is similar.
>>> ans = b1.kl_loss('Beta', concentration1_b, concentration0_b)
>>> print(ans.shape)
(3,)
>>> ans = b1.kl_loss('Beta', concentration1_b, concentration0_b, concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Additional `concentration1` and `concentration0` must be passed in.
>>> ans = b2.kl_loss('Beta', concentration1_b, concentration0_b, concentration1_a, concentration0_a)
>>> print(ans.shape)
(3,)
>>> # Examples of `sample`.
>>> # Args:
>>> #     shape (tuple): the shape of the sample. Default: ()
>>> #     concentration1 (Tensor): the concentration1 of the distribution. Default: self._concentration1.
>>> #     concentration0 (Tensor): the concentration0 of the distribution. Default: self._concentration0.
>>> ans = b1.sample()
>>> print(ans.shape)
(1,)
>>> ans = b1.sample((2,3))
>>> print(ans.shape)
(2, 3, 1)
>>> ans = b1.sample((2,3), concentration1_b, concentration0_b)
>>> print(ans.shape)
(2, 3, 3)
>>> ans = b2.sample((2,3), concentration1_a, concentration0_a)
>>> print(ans.shape)
(2, 3, 3)

property concentration0

Return concentration0, aka the beta parameter of the Beta distribution.

Returns

Tensor, the value of concentration0.

property concentration1

Return concentration1, aka the alpha parameter of the Beta distribution.

Returns

Tensor, the value of concentration1.

cdf(value, concentration1, concentration0)

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

Parameters

value (Tensor) - the value to compute.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

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

cross_entropy(dist, concentration1_b, concentration0_b, concentration1, concentration0)

Compute the cross entropy of two distribution

Parameters

dist (str) - the type of the other distribution.
concentration1_b (Tensor) - the alpha parameter of the other Beta distribution.
concentration0_b (Tensor) - the beta parameter of the other Beta distribution.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the value of the cross entropy.

entropy(concentration1, concentration0)

Compute the value of the entropy.

Parameters

concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the value of the entropy.

kl_loss(dist, concentration1_b, concentration0_b, concentration1, concentration0)

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

Parameters

dist (str) - the type of the other distribution.
concentration1_b (Tensor) - the alpha parameter of the other Beta distribution.
concentration0_b (Tensor) - the beta parameter of the other Beta distribution.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

log_cdf(value, concentration1, concentration0)

Compute the log value of the cumulatuve distribution function.

Parameters

value (Tensor) - the value to compute.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the log value of the cumulatuve distribution function.

log_prob(value, concentration1, concentration0)

the log value of the probability.

Parameters

value (Tensor) - the value to compute.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the log value of the probability.

log_survival(value, concentration1, concentration0)

Compute the log value of the survival function.

Parameters

value (Tensor) - the value to compute.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

mean(concentration1, concentration0)

Compute the mean value of the distribution.

Parameters

concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the mean of the distribution.

mode(concentration1, concentration0)

Compute the mode value of the distribution.

Parameters

concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the mode of the distribution.

prob(value, concentration1, concentration0)

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

Parameters

value (Tensor) - the value to compute.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the value of the probability.

sample(shape, concentration1, concentration0)

Generate samples.

Parameters

shape (tuple) - the shape of the sample.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the sample following the distribution.

sd(concentration1, concentration0)

The standard deviation.

Parameters

concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the standard deviation of the distribution.

survival_function(value, concentration1, concentration0)

Compute the value of the survival function.

Parameters

value (Tensor) - the value to compute.
concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the value of the survival function.

var(concentration1, concentration0)

Compute the variance of the distribution.

Parameters

concentration1 (Tensor) - the alpha parameter of the Beta distribution. Default value: None.
concentration0 (Tensor) - the beta parameter of the Beta distribution. Default value: None.

Returns

Tensor, the variance of the distribution.