The Hidden Markov Ising Model with Exogenous Covariates
Abstract
The Ising model, a type of Markov Random Field, from statistical physics has a long history of modeling spatial and network data as well as particle interactions. In this work, we consider inserting the Ising model into the framework of a Hidden Markov Model, a type of Bayesian Network, to model temporal state changes in a sequence of Ising observations. While this is entirely a discrete probability model, a main challenge is the fitting of such a probabilistic graphical model due to the exponential intractability of normalizing constants within the Ising model. To circumvent this problem, we consider the usage of maximum pseudolikelihood estimators that have a long history in Markov Random Fields. Validity of the pseudolikelihood Baum-Welch algorithm, model identifiability under likelihood, and consistency for large networks is also proved. The proposed Hidden Markov Ising Model is further extended to incorporate exogenous variables resulting in a hybrid hidden Markov autologistic model with graphical dependencies integrated into the model. This model is applied to a five year sequence of weekly gun violence events across the 3109 counties of the continental United States to identify state changes in gun violence activity from 2021 to 2025.
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BibTeX
@misc{vinayagasothy2026hidden,
title = {{The Hidden Markov Ising Model with Exogenous Covariates}},
author = {Aari Vinayagasothy and Beamlak Haddis and Oscar Lopez and Ann Manjo and Adam B Kashlak},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05213},
eprint = {2611.05213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05213},
}
RIS
TY - UNPB
TI - The Hidden Markov Ising Model with Exogenous Covariates
AU - Aari Vinayagasothy
AU - Beamlak Haddis
AU - Oscar Lopez
AU - Ann Manjo
AU - Adam B Kashlak
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05213
UR - https://arxiv.org/abs/2611.05213
AB - The Ising model, a type of Markov Random Field, from statistical physics has a long history of modeling spatial and network data as well as particle interactions. In this work, we consider inserting the Ising model into the framework of a Hidden Markov Model, a type of Bayesian Network, to model temporal state changes in a sequence of Ising observations. While this is entirely a discrete probability model, a main challenge is the fitting of such a probabilistic graphical model due to the exponential intractability of normalizing constants within the Ising model. To circumvent this problem, we consider the usage of maximum pseudolikelihood estimators that have a long history in Markov Random Fields. Validity of the pseudolikelihood Baum-Welch algorithm, model identifiability under likelihood, and consistency for large networks is also proved. The proposed Hidden Markov Ising Model is further extended to incorporate exogenous variables resulting in a hybrid hidden Markov autologistic model with graphical dependencies integrated into the model. This model is applied to a five year sequence of weekly gun violence events across the 3109 counties of the continental United States to identify state changes in gun violence activity from 2021 to 2025.
ER -