tf.compat.v1.distributions.Multinomial

Multinomial distribution.

Inherits From: Distribution

tf.compat.v1.distributions.Multinomial(
    total_count, logits=None, probs=None, validate_args=False, allow_nan_stats=True,
    name='Multinomial'
)

This Multinomial distribution is parameterized by probs, a (batch of) length-K prob (probability) vectors (K > 1) such that tf.reduce_sum(probs, -1) = 1, and a total_count number of trials, i.e., the number of trials per draw from the Multinomial. It is defined over a (batch of) length-K vector counts such that tf.reduce_sum(counts, -1) = total_count. The Multinomial is identically the Binomial distribution when K = 2.

Mathematical Details

The Multinomial is a distribution over K-class counts, i.e., a length-K vector of non-negative integer counts = n = [n_0, ..., n_{K-1}].

The probability mass function (pmf) is,

pmf(n; pi, N) = prod_j (pi_j)**n_j / Z
Z = (prod_j n_j!) / N!

where:

probs = pi = [pi_0, ..., pi_{K-1}], pi_j > 0, sum_j pi_j = 1,
total_count = N, N a positive integer,
Z is the normalization constant, and,
N! denotes N factorial.

Distribution parameters are automatically broadcast in all functions; see examples for details.

Pitfalls

The number of classes, K, must not exceed:

the largest integer representable by self.dtype, i.e., 2**(mantissa_bits+1) (IEE754),
the maximum Tensor index, i.e., 2**31-1.

In other words,

K <= min(2**31-1, {
  tf.float16: 2**11,
  tf.float32: 2**24,
  tf.float64: 2**53 }[param.dtype])

Note: This condition is validated only when self.validate_args = True.

Examples

Create a 3-class distribution, with the 3rd class is most likely to be drawn, using logits.

logits = [-50., -43, 0]
dist = Multinomial(total_count=4., logits=logits)

Create a 3-class distribution, with the 3rd class is most likely to be drawn.

p = [.2, .3, .5]
dist = Multinomial(total_count=4., probs=p)

The distribution functions can be evaluated on counts.

# counts same shape as p.
counts = [1., 0, 3]
dist.prob(counts)  # Shape []

# p will be broadcast to [[.2, .3, .5], [.2, .3, .5]] to match counts.
counts = [[1., 2, 1], [2, 2, 0]]
dist.prob(counts)  # Shape [2]

# p will be broadcast to shape [5, 7, 3] to match counts.
counts = [[...]]  # Shape [5, 7, 3]
dist.prob(counts)  # Shape [5, 7]

Create a 2-batch of 3-class distributions.

p = [[.1, .2, .7], [.3, .3, .4]]  # Shape [2, 3]
dist = Multinomial(total_count=[4., 5], probs=p)

counts = [[2., 1, 1], [3, 1, 1]]
dist.prob(counts)  # Shape [2]

dist.sample(5) # Shape [5, 2, 3]

Args
`total_count`	Non-negative floating point tensor with shape broadcastable to `[N1,..., Nm]` with `m >= 0`. Defines this as a batch of `N1 x ... x Nm` different Multinomial distributions. Its components should be equal to integer values.
`logits`	Floating point tensor representing unnormalized log-probabilities of a positive event with shape broadcastable to `[N1,..., Nm, K]` `m >= 0`, and the same dtype as `total_count`. Defines this as a batch of `N1 x ... x Nm` different `K` class Multinomial distributions. Only one of `logits` or `probs` should be passed in.
`probs`	Positive floating point tensor with shape broadcastable to `[N1,..., Nm, K]` `m >= 0` and same dtype as `total_count`. Defines this as a batch of `N1 x ... x Nm` different `K` class Multinomial distributions. `probs`'s components in the last portion of its shape should sum to `1`. Only one of `logits` or `probs` should be passed in.
`validate_args`	Python `bool`, default `False`. When `True` distribution parameters are checked for validity despite possibly degrading runtime performance. When `False` invalid inputs may silently render incorrect outputs.
`allow_nan_stats`	Python `bool`, default `True`. When `True`, statistics (e.g., mean, mode, variance) use the value "`NaN`" to indicate the result is undefined. When `False`, an exception is raised if one or more of the statistic's batch members are undefined.
`name`	Python `str` name prefixed to Ops created by this class.

Attributes
`allow_nan_stats`	Python `bool` describing behavior when a stat is undefined. Stats return +/- infinity when it makes sense. E.g., the variance of a Cauchy distribution is infinity. However, sometimes the statistic is undefined, e.g., if a distribution's pdf does not achieve a maximum within the support of the distribution, the mode is undefined. If the mean is undefined, then by definition the variance is undefined. E.g. the mean for Student's T for df = 1 is undefined (no clear way to say it is either + or - infinity), so the variance = E[(X - mean)**2] is also undefined.
`batch_shape`	Shape of a single sample from a single event index as a `TensorShape`. May be partially defined or unknown. The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
`dtype`	The `DType` of `Tensor`s handled by this `Distribution`.
`event_shape`	Shape of a single sample from a single batch as a `TensorShape`. May be partially defined or unknown.
`logits`	Vector of coordinatewise logits.
`name`	Name prepended to all ops created by this `Distribution`.
`parameters`	Dictionary of parameters used to instantiate this `Distribution`.
`probs`	Probability of drawing a `1` in that coordinate.
`reparameterization_type`	Describes how samples from the distribution are reparameterized. Currently this is one of the static instances `distributions.FULLY_REPARAMETERIZED` or `distributions.NOT_REPARAMETERIZED`.
`total_count`	Number of trials used to construct a sample.
`validate_args`	Python `bool` indicating possibly expensive checks are enabled.

Args
`value`	`float` or `double` `Tensor`.
`name`	Python `str` prepended to names of ops created by this function.

Args
`other`	`tfp.distributions.Distribution` instance.
`name`	Python `str` prepended to names of ops created by this function.

Args
`sample_shape`	`Tensor` or python list/tuple. Desired shape of a call to `sample()`.
`name`	name to prepend ops with.

Args
`sample_shape`	0D or 1D `int32` `Tensor`. Shape of the generated samples.
`seed`	Python integer seed for RNG
`name`	name to give to the op.

tf.compat.v1.distributions.Multinomial

Mathematical Details

Pitfalls

Examples

Methods

batch_shape_tensor

cdf

copy

covariance

cross_entropy

entropy

event_shape_tensor

is_scalar_batch

is_scalar_event

kl_divergence

log_cdf

log_prob

log_survival_function

mean

mode

param_shapes

param_static_shapes

prob

quantile

sample

stddev

survival_function

variance

`batch_shape_tensor`

`cdf`

`copy`

`covariance`

`cross_entropy`

`entropy`

`event_shape_tensor`

`is_scalar_batch`

`is_scalar_event`

`kl_divergence`

`log_cdf`

`log_prob`

`log_survival_function`

`mean`

`mode`

`param_shapes`

`param_static_shapes`

`prob`

`quantile`

`sample`

`stddev`

`survival_function`

`variance`