A Characterization of the Dirichlet Distribution with Application to Learning Bayesian Networks

TL;DR

This paper offers a new way to understand the Dirichlet distribution, showing that certain assumptions in learning belief networks naturally lead to using a Dirichlet prior, emphasizing its fundamental role.

Contribution

It introduces a novel characterization of the Dirichlet distribution and demonstrates its inevitability in Bayesian network learning under common assumptions.

Findings

Dirichlet distribution characterized in a new way

Dirichlet prior is inevitable under certain learning assumptions

Implications for Bayesian network parameter learning

Abstract

We provide a new characterization of the Dirichlet distribution. This characterization implies that under assumptions made by several previous authors for learning belief networks, a Dirichlet prior on the parameters is inevitable.