@inproceedings{fe86635353834605a3d67cd7bc0c34eb,
title = "On Functions of Markov Random Fields",
abstract = "We derive two sufficient conditions for a function of a Markov random field (MRF) on a given graph to be a MRF on the same graph. The first condition is information-theoretic and parallels a recent information-theoretic characterization of lumpability of Markov chains. The second condition, which is easier to check, is based on the potential functions of the corresponding Gibbs field. We illustrate our sufficient conditions at the hand of several examples and discuss implications for practical applications of MRFs. As a side result, we give a partial characterization of functions of MRFs that are information preserving.",
keywords = "Gibbs field, Hidden Markov random field, Lumpability, Markov random field",
author = "Bernhard Geiger and Ali Al-Bashabsheh",
year = "2021",
month = apr,
day = "11",
doi = "10.1109/ITW46852.2021.9457677",
language = "English",
series = "2020 IEEE Information Theory Workshop, ITW 2020",
pages = "316--320",
booktitle = "2020 IEEE Information Theory Workshop, ITW 2020",
note = "2020 IEEE Information Theory Workshop : ITW 2020, ITW 2020 ; Conference date: 11-04-2021 Through 15-04-2021",
}