# Bayesian Higher Order Hidden Markov Models

arXiv: https://arxiv.org/abs/1805.12201 · HTML: https://mlsanity.com/paper/1805.12201/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2018.

## Built on by (most cited first, 1 of 1)

- [Bayesian Detection of Mesoscale Structures in Pathway Data on Graphs](https://mlsanity.com/paper/2301.11120/) (2023)

## Abstract (arXiv)

We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology based on tensor factorization techniques that can characterize any transition probability with a specified maximal order, allowing automated selection of the important lags and capturing higher order interactions among the lags. Theoretical results provide insights into identifiability of the emission distributions and asymptotic behavior of the posterior. We design efficient Markov chain Monte Carlo algorithms for posterior computation. In simulation experiments, the method vastly outperformed its first and higher order competitors not just in higher order settings, but, remarkably, also in first order cases. Practical utility is illustrated using real world applications.