A reversible infinite HMM using normalised random measures

TL;DR

This paper introduces a nonparametric prior for reversible Markov chains using gamma processes, enabling the construction of a reversible infinite Hidden Markov Model with applications in epigenomics and ion channel data analysis.

Contribution

It presents a novel nonparametric prior over reversible Markov chains based on gamma processes, facilitating efficient inference for reversible infinite HMMs.

Findings

Successfully applied to epigenomics data

Demonstrated effectiveness on ion channel recordings

Provides a new framework for reversible Markov models

Abstract

We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Markov chain. The resulting prior over infinite transition matrices is closely related to the hierarchical Dirichlet process but enforces reversibility. A reinforcement scheme has recently been proposed with similar properties, but the de Finetti measure is not well characterised. We take the alternative approach of explicitly constructing the mixing measure, which allows more straightforward and efficient inference at the cost of no longer having a closed form predictive distribution. We use our process to construct a reversible infinite HMM which we apply to two real datasets, one from epigenomics and one ion channel recording.