Optimal Nonlinear Prediction of Random Fields on Networks

TL;DR

This paper develops an information-theoretic framework for optimal nonlinear prediction of time-varying random fields on networks, introducing local sufficient statistics and an algorithm for their empirical estimation.

Contribution

It formalizes the prediction problem as finding minimal local sufficient statistics and provides a convergent algorithm for their estimation from data without distributional assumptions.

Findings

Local sufficient statistics can be composed into global predictors.

The proposed algorithm converges with minimal prior information.

The approach applies to discrete-valued 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.