Gumbel¶

class paddle.distribution. Gumbel ( loc: float | Tensor, scale: float | Tensor ) [source]

The Gumbel distribution with location loc and scale parameters.

Mathematical details

The probability density function (pdf) is

$$pdf(x; mu, sigma) = exp(-(x - mu) / sigma - exp(-(x - mu) / sigma)) / sigma$$

In the above equation:

• $loc = \mu$: is the mean.

• $scale = \sigma$: is the std.

Parameters

• loc (int|float|tensor) – The mean of gumbel distribution.The data type is int, float, tensor.

• scale (int|float|tensor) – The std of gumbel distribution.The data type is int, float, tensor.

Examples

>>> import paddle
>>> from paddle.distribution.gumbel import Gumbel

>>> # Gumbel distributed with loc=0, scale=1
>>> dist = Gumbel(paddle.full([1], 0.0), paddle.full([1], 1.0))

>>> 
>>> print(dist.sample([2]))
Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True,
[[0.40484068],
[3.19400501]])

>>> print(dist.rsample([2]))
Tensor(shape=[2, 1], dtype=float32, place=Place(cpu), stop_gradient=True,
[[-0.95093185],
[ 0.32422572]])

>>> 
>>> value = paddle.full([1], 0.5)
>>> print(dist.prob(value))
Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
[0.33070430])

>>> print(dist.log_prob(value))
Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
[-1.10653067])

>>> print(dist.cdf(value))
Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
[0.54523921])

>>> print(dist.entropy())
Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
[1.57721567])

property mean : Tensor

Mean of distribution

The mean is

$$mean = \mu + \sigma * γ$$

In the above equation:

• $loc = \mu$: is the location parameter.

• $scale = \sigma$: is the scale parameter.

• $γ$: is the euler’s constant.

Returns

mean value.

Return type

Tensor

property variance : Tensor

Variance of distribution.

The variance is

$$variance = \sigma^2 * \pi^2 / 6$$

In the above equation:

• $scale = \sigma$: is the scale parameter.

Returns

The variance value.

Return type

Tensor

property stddev : Tensor

Standard deviation of distribution

The standard deviation is

$$stddev = \sqrt{\sigma^2 * \pi^2 / 6}$$

In the above equation: * $scale = \sigma$: is the scale parameter.

Returns

std value

Return type

Tensor

property batch_shape : Sequence[int]

Returns batch shape of distribution

Returns

batch shape

Return type

Sequence[int]

property event_shape : Sequence[int]

Returns event shape of distribution

Returns

event shape

Return type

Sequence[int]

kl_divergence ( other: Distribution ) → Tensor [source]

kl_divergence¶

The KL-divergence between self distributions and other.

prob ( value: Tensor ) → Tensor

prob¶

Probability density/mass function

Parameters

value (Tensor) – The input tensor.

Returns

probability.The data type is same with value.

Return type

Tensor

probs ( value: Tensor ) → Tensor

probs¶

Probability density/mass function.

Note

This method will be deprecated in the future, please use prob instead.

log_prob ( value: Tensor ) → Tensor

log_prob¶

Log probability density/mass function.

Parameters

value (Tensor) – The input tensor.

Returns

log probability.The data type is same with value.

Return type

Tensor

cdf ( value: Tensor ) → Tensor

cdf¶

Cumulative distribution function. :param value: value to be evaluated. :type value: Tensor

Returns

cumulative probability of value.

Return type

Tensor

entropy ( ) → Tensor

entropy¶

Entropy of Gumbel distribution.

Returns

Entropy of distribution.

sample ( shape: Sequence[int] = [] ) → Tensor

sample¶

Sample from Gumbel.

Parameters

shape (Sequence[int], optional) – The sample shape. Defaults to [].

Returns

A tensor with prepended dimensions shape.The data type is float32.

Return type

Tensor

rsample ( shape: Sequence[int] = [] ) → Tensor

rsample¶

reparameterized sample :param shape: 1D int32. Shape of the generated samples. Defaults to []. :type shape: Sequence[int], optional

Returns

A tensor with prepended dimensions shape.The data type is float32.

Return type

Tensor