Optimal Nonlinear Prediction of Random Fields on Networks
Abstract
It is increasingly common to encounter time-varying random fields on networks (metabolic networks, sensor arrays, distributed computing, etc.). This paper considers the problem of optimal, nonlinear prediction of these fields, showing from an information-theoretic perspective that it is formally identical to the problem of finding minimal local sufficient statistics. I derive general properties of these statistics, show that they can be composed into global predictors, and explore their recursive estimation properties. For the special case of discrete-valued fields, I describe a convergent algorithm to identify the local predictors from empirical data, with minimal prior information about the field, and no distributional assumptions.
Cite
@article{arxiv.math/0305160,
title = {Optimal Nonlinear Prediction of Random Fields on Networks},
author = {Cosma Rohilla Shalizi},
journal= {arXiv preprint arXiv:math/0305160},
year = {2022}
}
Comments
20 pages, 5 figures. For the conference "Discrete Models of Complex Systems" (Lyon, June, 2003). v2: Typos fixed, regenerated figures should now produce readable PDF output