Bernoulli¶

class paddle.distribution. Bernoulli ( probs, name=None ) [source]

Bernoulli distribution parameterized by probs, which is the probability of value 1.

In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q=1-p.

The probability mass function of this distribution, over possible outcomes k, is

\[\begin{split}{\begin{cases} q=1-p & \text{if }value=0 \\ p & \text{if }value=1 \end{cases}}\end{split}\]

Parameters

probs (float|Tensor) – The probs input of Bernoulli distribution. The data type is float32 or float64. The range must be in [0, 1].
name (str, optional) – Name for the operation (optional, default is None). For more information, please refer to Name.

Examples

           import paddle
from paddle.distribution import Bernoulli

# init `probs` with a float
rv = Bernoulli(probs=0.3)

print(rv.mean)
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        0.30000001)

print(rv.variance)
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        0.21000001)

print(rv.entropy())
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        0.61086434)

          

probs ( value ) probs¶: Probability density/mass function.

Note

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

property mean

Mean of Bernoulli distribution.

Returns: Mean value of distribution.
Return type: Tensor

property variance

Variance of Bernoulli distribution.

Returns: Variance value of distribution.
Return type: Tensor

sample ( shape ) sample¶

Sample from Bernoulli distribution.

Parameters: shape (Sequence[int]) – Sample shape.
Returns: Sampled data with shape sample_shape + batch_shape + event_shape.
Return type: Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

rv = Bernoulli(paddle.full((), 0.3))
print(rv.sample([100]).shape)
# [100]

rv = Bernoulli(paddle.to_tensor(0.3))
print(rv.sample([100]).shape)
# [100, 1]

rv = Bernoulli(paddle.to_tensor([0.3, 0.5]))
print(rv.sample([100]).shape)
# [100, 2]

rv = Bernoulli(paddle.to_tensor([0.3, 0.5]))
print(rv.sample([100, 2]).shape)
# [100, 2, 2]

            

rsample ( shape, temperature=1.0 ) rsample¶

Sample from Bernoulli distribution (reparameterized).

The rsample is a continuously approximate of Bernoulli distribution reparameterized sample method. [1] Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables. 2016. [2] Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with Gumbel-Softmax. 2016.

Note

rsample need to be followed by a sigmoid, which converts samples’ value to unit interval (0, 1).

Parameters

shape (Sequence[int]) – Sample shape.
temperature (float) – temperature for rsample, must be positive.

Returns

Sampled data with shape sample_shape + batch_shape + event_shape.

Return type

Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

paddle.seed(2023)

rv = Bernoulli(paddle.full((), 0.3))
print(rv.sample([100]).shape)
# [100]

rv = Bernoulli(0.3)
print(rv.rsample([100]).shape)
# [100, 1]

rv = Bernoulli(paddle.to_tensor([0.3, 0.5]))
print(rv.rsample([100]).shape)
# [100, 2]

rv = Bernoulli(paddle.to_tensor([0.3, 0.5]))
print(rv.rsample([100, 2]).shape)
# [100, 2, 2]

# `rsample` has to be followed by a `sigmoid`
rv = Bernoulli(0.3)
rsample = rv.rsample([3, ])
rsample_sigmoid = paddle.nn.functional.sigmoid(rsample)
print(rsample, rsample_sigmoid)
# Tensor(shape=[3, 1], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[-0.88315082],
#         [-0.62347704],
#         [-0.31513220]]) Tensor(shape=[3, 1], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [[0.29252526],
#         [0.34899110],
#         [0.42186251]])

# The smaller the `temperature`, the distribution of `rsample` closer to `sample`, with `probs` of 0.3.
print(paddle.nn.functional.sigmoid(rv.rsample([1000, ], temperature=1.0)).sum())
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        361.06829834)

print(paddle.nn.functional.sigmoid(rv.rsample([1000, ], temperature=0.1)).sum())
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        288.66418457)

            

cdf ( value ) cdf¶

Cumulative distribution function(CDF) evaluated at value.

\[\begin{split}{ \begin{cases} 0 & \text{if } value \lt 0 \\ 1 - p & \text{if } 0 \leq value \lt 1 \\ 1 & \text{if } value \geq 1 \end{cases} }\end{split}\]

Parameters: value (Tensor) – Value to be evaluated.
Returns: CDF evaluated at value.
Return type: Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

rv = Bernoulli(0.3)
print(rv.cdf(paddle.to_tensor([1.0])))
# Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [1.])

            

log_prob ( value ) log_prob¶

Log of probability densitiy function.

Parameters: value (Tensor) – Value to be evaluated.
Returns: Log of probability densitiy evaluated at value.
Return type: Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

rv = Bernoulli(0.3)
print(rv.log_prob(paddle.to_tensor([1.0])))
# Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [-1.20397282])

            

property batch_shape

Returns batch shape of distribution

Returns: batch shape
Return type: Sequence[int]

property event_shape

Returns event shape of distribution

Returns: event shape
Return type: Sequence[int]

prob ( value ) prob¶

Probability density function(PDF) evaluated at value.

\[\begin{split}{ \begin{cases} q=1-p & \text{if }value=0 \\ p & \text{if }value=1 \end{cases} }\end{split}\]

Parameters: value (Tensor) – Value to be evaluated.
Returns: PDF evaluated at value.
Return type: Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

rv = Bernoulli(0.3)
print(rv.prob(paddle.to_tensor([1.0])))
# Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,
#        [0.29999998])

            

entropy ( ) entropy¶

Entropy of Bernoulli distribution.

\[{ entropy = -(q \log q + p \log p) }\]

Returns: Entropy of distribution.
Return type: Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

rv = Bernoulli(0.3)
print(rv.entropy())
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        0.61086434)

            

kl_divergence ( other ) [source] kl_divergence¶

The KL-divergence between two Bernoulli distributions.

\[{ KL(a || b) = p_a \log(p_a / p_b) + (1 - p_a) \log((1 - p_a) / (1 - p_b)) }\]

Parameters: other (Bernoulli) – instance of Bernoulli.
Returns: kl-divergence between two Bernoulli distributions.
Return type: Tensor

Examples

             import paddle
from paddle.distribution import Bernoulli

rv = Bernoulli(0.3)
rv_other = Bernoulli(0.7)

print(rv.kl_divergence(rv_other))
# Tensor(shape=[], dtype=float32, place=Place(cpu), stop_gradient=True,
#        0.33891910)

            

Bernoulli¶

probs¶

sample¶

rsample¶

cdf¶

log_prob¶

prob¶

entropy¶

kl_divergence¶