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mindspore.nn.probability.distribution.Beta

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

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' .

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.

Supported Platforms:

Ascend

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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: 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: None .

• concentration0 (Tensor) - the beta parameter of the Beta distribution. Default: None .

Returns

Tensor, the variance of the distribution.