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.
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Michel Morvan and Éric Rémila. Discrete Models for Complex Systems, DMCS'03, 2003, Lyon, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), pp.11-30, 2003, DMTCS Proceedings
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Cosma Rohilla Shalizi. Optimal Nonlinear Prediction of Random Fields on Networks. Michel Morvan and Éric Rémila. Discrete Models for Complex Systems, DMCS'03, 2003, Lyon, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03), pp.11-30, 2003, DMTCS Proceedings. 〈hal-01183318〉

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