Optimal Nonlinear Prediction of Random Fields on Networks

Cosma Rohilla Shalizi

doi:10.46298/dmtcs.2310

Cosma Rohilla Shalizi - Optimal Nonlinear Prediction of Random Fields on Networks

dmtcs:2310 - Discrete Mathematics & Theoretical Computer Science, January 1, 2003, DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03) - https://doi.org/10.46298/dmtcs.2310

Optimal Nonlinear Prediction of Random Fields on NetworksArticle

Authors: Cosma Rohilla Shalizi ¹

1 Center for the study of complex systems

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.

https://doi.org/10.46298/dmtcs.2310

Source: HAL:hal-01183318v1

Volume: DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03)

Section: Proceedings

Published on: January 1, 2003

Imported on: November 21, 2016

Keywords: recursive estimation,Networks,random fields,sufficient statistics,nonlinear prediction,information theory,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[NLIN.NLIN-CG] Nonlinear Sciences [physics]/Cellular Automata and Lattice Gases [nlin.CG],[INFO.INFO-HC] Computer Science [cs]/Human-Computer Interaction [cs.HC]

Classifications

Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

Bibliographic References

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