Cruising The Simplex: Hamiltonian Monte Carlo and the Dirichlet Distribution

TL;DR

This paper introduces transformations that simplify the Dirichlet distribution, making it more compatible with Hamiltonian Monte Carlo methods for efficient sampling in constrained spaces.

Contribution

The paper presents novel transformations that convert the Dirichlet distribution into a form better suited for MCMC algorithms like Hamiltonian Monte Carlo.

Findings

Transformations improve MCMC sampling efficiency for Dirichlet distributions

Enhanced compatibility of Dirichlet with Hamiltonian Monte Carlo

Potential for broader application in constrained probabilistic models

Abstract

Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo. I demonstrate a series of transformations that reshape the canonical Dirichlet distribution into a form much more amenable to MCMC algorithms.