Dirichlet distribution

Creator

Creator

Created

Created

2023 Apr 4 2:29

Editor

Editor

Edited

Edited

2025 Mar 12 12:26

Refs

Refs

Categorical distribution

Decoding Strategy

Exponential family distribution over the
Probability simplex, essentially a distribution over multinomial distributions.

A set of probability distributions used to model probabilities for each class in multiclass problems and describe proportions

Specific case of

Beta Distribution

P(\boldsymbol{\theta} \mid \boldsymbol{\alpha}) =\frac{\Gamma \left( \sum_{k=1}^{K} \alpha_k \right)}{\prod_{k=1}^{K} \Gamma (\alpha_k)}\prod_{k=1}^{K} \theta_k^{\alpha_k - 1}\\ \text{where } \Gamma(n) = (n - 1)!

$\alpha$ controls the mean shape and sparsity of $\theta$

Value of $\alpha < 1$ create increasingly sparse outputs

Conjugate Prior of the
Multinomial distribution

Dirichlet distribution

In probability and statistics, the Dirichlet distribution, often denoted , is a family of continuous multivariate probability distributions parameterized by a vector of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.

Dirichlet distribution

https://en.wikipedia.org/wiki/Dirichlet_distribution

Dirichlet distribution

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