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  1. Home > Articles & Issues >
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  3. Optimal Nonlinear Pr ...
Conference paper

Optimal Nonlinear Prediction of Random Fields on Networks

Cosma Rohilla Shalizi ORCID (1)
(1) Center for the study of complex systems
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Imported on
November 21, 2016
Published on
December 31, 2002
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AB, Discrete Models for Complex Systems (DMCS'03)
Proceedings
DOI
10.46298/dmtcs.2310
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https://about.hal.science/hal-authorisation-v1
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Optimal Nonlinear Prediction of Random Fields on Networks

Cosma Rohilla Shalizi ORCID (1)
(1) Center for the study of complex systems
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.
Keywords
  • [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]
  • recursive estimation
  • Networks
  • random fields
  • sufficient statistics
  • nonlinear prediction
  • information theory
Mathematics Subject Classification 2020
  • 05A05 - Permutations, words, matrices
  • 05A15 - Exact enumeration problems, generating functions
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