Multinomial¶
- class paddle.distribution. Multinomial ( total_count, probs ) [source]
-
Multinomial distribution parameterized by
total_countandprobs.In probability theory, the multinomial distribution is a generalization of the binomial distribution, it models the probability of counts for each side of a k-sided die rolled n times. When k is 2 and n is 1, the multinomial is the bernoulli distribution, when k is 2 and n is grater than 1, it is the binomial distribution, when k is grater than 2 and n is 1, it is the categorical distribution.
The probability mass function (PMF) for multinomial is
\[f(x_1, ..., x_k; n, p_1,...,p_k) = \frac{n!}{x_1!...x_k!}p_1^{x_1}...p_k^{x_k}\]where, \(n\) is number of trials, k is the number of categories, \(p_i\) denote probability of a trial falling into each category, \({\textstyle \sum_{i=1}^{k}p_i=1}, p_i \ge 0\), and \(x_i\) denote count of each category.
- Parameters
-
total_count (int) – Number of trials.
probs (Tensor) – Probability of a trial falling into each category. Last axis of probs indexes over categories, other axes index over batches. Probs value should between [0, 1], and sum to 1 along last axis. If the value over 1, it will be normalized to sum to 1 along the last axis.
Examples:
>>> import paddle >>> paddle.seed(2023) >>> multinomial = paddle.distribution.Multinomial(10, paddle.to_tensor([0.2, 0.3, 0.5])) >>> print(multinomial.sample((2, 3))) Tensor(shape=[2, 3, 3], dtype=float32, place=Place(cpu), stop_gradient=True, [[[1., 5., 4.], [0., 4., 6.], [1., 3., 6.]], [[2., 2., 6.], [0., 6., 4.], [3., 3., 4.]]])
-
probs
(
value
)
probs¶
-
Probability density/mass function.
Note
This method will be deprecated in the future, please use prob instead.
- property mean
-
mean of multinomial distribuion.
- Returns
-
mean value.
- Return type
-
Tensor
- property variance
-
variance of multinomial distribution.
- Returns
-
variance value.
- Return type
-
Tensor
-
prob
(
value
)
prob¶
-
probability mass function evaluated at value.
- Parameters
-
value (Tensor) – value to be evaluated.
- Returns
-
probability of value.
- Return type
-
Tensor
-
log_prob
(
value
)
log_prob¶
-
probability mass function evaluated at value
- Parameters
-
value (Tensor) – value to be evaluated.
- Returns
-
probability of value.
- Return type
-
Tensor
-
sample
(
shape=()
)
sample¶
-
draw sample data from multinomial distribution
- Parameters
-
sample_shape (tuple, optional) – [description]. Defaults to ().
-
entropy
(
)
entropy¶
-
entropy of multinomial distribution
- Returns
-
entropy value
- Return type
-
Tensor
- 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]
-
kl_divergence
(
other
)
[source]
kl_divergence¶
-
The KL-divergence between self distributions and other.
-
rsample
(
shape=()
)
rsample¶
-
reparameterized sample