# Diffusion Adaptation Strategies for Distributed Estimation over Gaussian Markov Random Fields

arXiv: https://arxiv.org/abs/1407.3698 · HTML: https://mlsanity.com/paper/1407.3698/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2014.

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

- [Colored Markov Random Fields for Probabilistic Topological Modeling](https://mlsanity.com/paper/2512.03727/) (2025)

## Abstract (arXiv)

The aim of this paper is to propose diffusion strategies for distributed estimation over adaptive networks, assuming the presence of spatially correlated measurements distributed according to a Gaussian Markov random field (GMRF) model. The proposed methods incorporate prior information about the statistical dependency among observations, while at the same time processing data in real-time and in a fully decentralized manner. A detailed mean-square analysis is carried out in order to prove stability and evaluate the steady-state performance of the proposed strategies. Finally, we also illustrate how the proposed techniques can be easily extended in order to incorporate thresholding operators for sparsity recovery applications. Numerical results show the potential advantages of using such techniques for distributed learning in adaptive networks deployed over GMRF.