Discrete approximation of a mixture distribution via restricted divergence

TL;DR

This paper introduces the DIRECT algorithm, which constructs a discrete mixture distribution approximation with guaranteed precision in terms of Kullback-Leibler divergence, useful for simplifying complex mixture models.

Contribution

The paper presents a novel algorithm for approximating complex mixture distributions with discrete mixtures while controlling approximation error.

Findings

The DIRECT algorithm guarantees a specified divergence threshold.

Application examples demonstrate the method's effectiveness.

The approach simplifies complex mixture models for practical use.

Abstract

Mixture distributions arise in many application areas, for example as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a mixture distribution with a large to infinite number, discrete or continuous, of components. The proposed DIRECT (Divergence Restricting Conditional Tesselation) algorithm is set up such that a pre-specified precision, defined in terms of Kullback-Leibler divergence between true distribution and approximation, is guaranteed. Application of the algorithm is demonstrated in two examples.