DirichletMultinomial - LostTech.TensorFlow Documentation

Type DirichletMultinomial

Namespace tensorflow.distributions

Dirichlet-Multinomial compound distribution.

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

#### Mathematical Details

The Dirichlet-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,

```none pmf(n; alpha, N) = Beta(alpha + n) / (prod_j n_j!) / Z Z = Beta(alpha) / N! ```

where:

* `concentration = alpha = [alpha_0,..., alpha_{K-1}]`, `alpha_j > 0`, * `total_count = N`, `N` a positive integer, * `N!` is `N` factorial, and, * `Beta(x) = prod_j Gamma(x_j) / Gamma(sum_j x_j)` is the [multivariate beta function]( https://en.wikipedia.org/wiki/Beta_function#Multivariate_beta_function), and, * `Gamma` is the [gamma function]( https://en.wikipedia.org/wiki/Gamma_function).

Dirichlet-Multinomial is a [compound distribution]( https://en.wikipedia.org/wiki/Compound_probability_distribution), i.e., its samples are generated as follows.

1. Choose class probabilities: `probs = [p_0,...,p_{K-1}] ~ Dir(concentration)` 2. Draw integers: `counts = [n_0,...,n_{K-1}] ~ Multinomial(total_count, probs)`

The last `concentration` dimension parametrizes a single Dirichlet-Multinomial distribution. When calling distribution functions (e.g., `dist.prob(counts)`), `concentration`, `total_count` and `counts` are broadcast to the same shape. The last dimension of `counts` corresponds single Dirichlet-Multinomial distributions.

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

#### Examples Creates a 3-class distribution, with the 3rd class is most likely to be drawn. The distribution functions can be evaluated on counts. Creates a 2-batch of 3-class distributions.

Show Example

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

Properties

Public properties

object allow_nan_stats get;

object allow_nan_stats_dyn get;

TensorShape batch_shape get;

object batch_shape_dyn get;

object concentration get;

Concentration parameter; expected prior counts for that coordinate.

object concentration_dyn get;

Concentration parameter; expected prior counts for that coordinate.

object dtype get;

object dtype_dyn get;

TensorShape event_shape get;

object event_shape_dyn get;

string name get;

object name_dyn get;

IDictionary<object, object> parameters get;

object parameters_dyn get;

object PythonObject get;

object reparameterization_type get;

object reparameterization_type_dyn get;

object total_concentration get;

Sum of last dim of concentration parameter.

object total_concentration_dyn get;