mindspore.nn.probability.distribution.Gumbel

class mindspore.nn.probability.distribution.Gumbel(loc, scale, seed=0, dtype=mstype.float32, name='Gumbel')[source]

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

\[f(x, a, b) = 1 / b \exp(\exp(-(x - a) / b) - x),\]

where a and b are loc and scale parameter respectively.

Parameters

loc (int, float, list, numpy.ndarray, Tensor) – The location of Gumbel distribution.
scale (int, float, list, numpy.ndarray, Tensor) – The scale of Gumbel distribution.
seed (int) – the seed used in sampling. The global seed is used if it is None. Default: 0.
dtype (mindspore.dtype) – type of the distribution. Default: mstype.float32.
name (str) – the name of the distribution. Default: ‘Gumbel’.

Inputs and Outputs of APIs:

The accessible APIs of the Gumbel 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 Gumbel distribution, please refer to mindspore.nn.probability.distribution.Distribution, and examples below.

Supported Platforms:

Ascend GPU

Note

scale must be greater than zero. dist_spec_args are loc and scale. dtype must be a float type because Gumbel distributions are continuous.

Raises

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

Examples

>>> import mindspore
>>> import numpy as np
>>> import mindspore.nn.probability.distribution as msd
>>> import mindspore.nn as nn
>>> from mindspore import Tensor
>>> class Prob(nn.Cell):
...     def __init__(self):
...         super(Prob, self).__init__()
...         self.gum = msd.Gumbel(np.array([0.0]), np.array([[1.0], [2.0]]), dtype=mindspore.float32)
...
...     def construct(self, x_):
...         return self.gum.prob(x_)
>>> value = np.array([1.0, 2.0]).astype(np.float32)
>>> pdf = Prob()
>>> output = pdf(Tensor(value, dtype=mindspore.float32))

property loc

Return the loc parameter of the distribution.

Returns

Tensor, the loc parameter of the distribution.

property scale

Return the scale parameter of the distribution.

Returns

Tensor, the scale parameter of the distribution.

cdf(value, loc, scale)

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

Parameters

value (Tensor) - the value to compute.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

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

cross_entropy(dist, loc_b, scale_b, loc, scale)

Compute the cross entropy of two distribution

Parameters

dist (str) - the type of the other distribution.
loc_b (Tensor) - the loc parameter of the other distribution.
scale_b (Tensor) - the scale parameter of the other distribution.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the cross entropy.

entropy(loc, scale)

Compute the value of the entropy.

Parameters

loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the entropy.

kl_loss(dist, loc_b, scale_b, loc, scale)

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

Parameters

dist (str) - the type of the other distribution.
loc_b (Tensor) - the loc parameter of the other distribution.
scale_b (Tensor) - the scale parameter of the other distribution.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

log_cdf(value, loc, scale)

Compute the log value of the cumulatuve distribution function.

Parameters

value (Tensor) - the value to compute.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the log value of the cumulatuve distribution function.

log_prob(value, loc, scale)

the log value of the probability.

Parameters

value (Tensor) - the value to compute.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the log value of the probability.

log_survival(value, loc, scale)

Compute the log value of the survival function.

Parameters

value (Tensor) - the value to compute.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the K-L loss.

mean(loc, scale)

Compute the mean value of the distribution.

Parameters

loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the mean of the distribution.

mode(loc, scale)

Compute the mode value of the distribution.

Parameters

loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the mode of the distribution.

prob(value, loc, scale)

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

Parameters

value (Tensor) - the value to compute.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the probability.

sample(shape, loc, scale)

Generate samples.

Parameters

shape (tuple) - the shape of the sample.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the sample following the distribution.

sd(loc, scale)

The standard deviation.

Parameters

loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the standard deviation of the distribution.

survival_function(value, loc, scale)

Compute the value of the survival function.

Parameters

value (Tensor) - the value to compute.
loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the value of the survival function.

var(loc, scale)

Compute the variance of the distribution.

Parameters

loc (Tensor) - the loc parameter of the distribution. Default value: None.
scale (Tensor) - the scale parameter of the distribution. Default value: None.

Returns

Tensor, the variance of the distribution.