# Determine the Number of States in Hidden Markov Models via Marginal Likelihood

arXiv: https://arxiv.org/abs/2405.12343 · HTML: https://mlsanity.com/paper/2405.12343/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2024.

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

- [Estimating the number of clusters of a Block Markov Chain](https://mlsanity.com/paper/2407.18287/) (2024)

## Abstract (arXiv)

Hidden Markov models (HMM) have been widely used by scientists to model stochastic systems: the underlying process is a discrete Markov chain and the observations are noisy realizations of the underlying process. Determining the number of hidden states for an HMM is a model selection problem, which is yet to be satisfactorily solved, especially for the popular Gaussian HMM with heterogeneous covariance. In this paper, we propose a consistent method for determining the number of hidden states of HMM based on the marginal likelihood, which is obtained by integrating out both the parameters and hidden states. Moreover, we show that the model selection problem of HMM includes the order selection problem of finite mixture models as a special case. We give rigorous proof of the consistency of the proposed marginal likelihood method and provide an efficient computation method for practical implementation. We numerically compare the proposed method with the Bayesian information criterion (BIC), demonstrating the effectiveness of the proposed marginal likelihood method.