Optimal Nonlinear Prediction of Random Fields on Networks

Details Optimal Nonlinear Prediction of Random Fields on Networks Optimal Nonlinear Prediction of Random Fields on Networks

2003-05-12

arxiv.org/abs/math/0305160v2

Discrete Mathematics and Theoretical Computer Science, vol. AB(DMCS), pp. 11--30 (2003)

Mathematics

Probability

20 pages, 5 figures. For the conference "Discrete Models of Complex Systems" (Lyon, June, 2003). v2: Typos fixed, regenerated

Scientific paper

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.

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