# Sparse Interaction Neighborhood Selection for Markov Random Fields via Reversible Jump and Pseudoposteriors

arXiv: https://arxiv.org/abs/2204.05933 · HTML: https://mlsanity.com/paper/2204.05933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 12 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [Nonparametric graphical model for counts](https://mlsanity.com/paper/1901.00886/) (2019)
- [Marginal Pseudo-Likelihood Learning of Markov Network structures](https://mlsanity.com/paper/1401.4988/) (2014)
- [Inference tools for Markov Random Fields on lattices: The R package mrf2d](https://mlsanity.com/paper/2006.00383/) (2020)
- [Prior specification of neighbourhood and interaction structure in binary Markov random fields](https://mlsanity.com/paper/1501.06344/) (2015)
- [A novel approach for Markov Random Field with intractable normalising constant on large lattices](https://mlsanity.com/paper/1601.02410/) (2016)
- [Efficient MCMC for Gibbs Random Fields using pre-computation](https://mlsanity.com/paper/1710.04093/) (2017)
- [Model comparison for Gibbs random fields using noisy reversible jump Markov chain Monte Carlo](https://mlsanity.com/paper/1712.05358/) (2017)

## Abstract (arXiv)

We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions based on relative positions of a two-dimensional lattice. Using a Bayesian framework, we propose a Reversible Jump Monte Carlo Markov Chain algorithm that jumps across subsets of a maximal range neighborhood, allowing us to perform model selection based on a marginal pseudoposterior distribution of models. To show the strength of our proposed methodology we perform a simulation study and apply it to a real dataset from a discrete texture image analysis.