Optimal Nonlinear Prediction of Random Fields on Networks

@inproceedings{Shalizi2003OptimalNP,
  title={Optimal Nonlinear Prediction of Random Fields on Networks},
  author={Cosma Rohilla Shalizi},
  booktitle={DMCS},
  year={2003}
}
  • C. Shalizi
  • Published in DMCS 12 May 2003
  • Computer Science
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… 

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References

SHOWING 1-10 OF 44 REFERENCES

Random Fields on a Network: Modeling, Statistics, and Applications

The theory of spatial models over lattices, or random fields as they are known, has developed significantly over recent years. This book provides a graduate-level introduction to the subject which

Toward a quantitative theory of self-generated complexity

TLDR
Quantities are defined operationally which qualify as measures of complexity of patterns arising in physical situations, and are essentially Shannon information needed to specify not individual patterns, but either measure-theoretic or algebraic properties of ensembles of pattern arising ina priori translationally invariant situations.

The Structure and Function of Complex Networks

TLDR
Developments in this field are reviewed, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

Graphical Models

TLDR
Some of the basic ideas underlying graphical models are reviewed, including the algorithmic ideas that allow graphical models to be deployed in large-scale data analysis problems and examples of graphical models in bioinformatics, error-control coding and language processing are presented.

An Algorithm for Pattern Discovery in Time Series

TLDR
A reliable procedure for building the minimal set of hidden, Markovian states that is statistically capable of producing the behavior exhibited in the data -- the underlying process's causal states.

Computational Mechanics: Pattern and Prediction, Structure and Simplicity

TLDR
It is shown that the causal-state representation—an ∈-machine—is the minimal one consistent with accurate prediction, and several results are established on ∉-machine optimality and uniqueness and on how∈-machines compare to alternative representations.

Predictive Representations of State

TLDR
This is the first specific formulation of the predictive idea that includes both stochasticity and actions (controls) and it is shown that any system has a linear predictive state representation with number of predictions no greater than the number of states in its minimal POMDP model.

Quantifying self-organization in cyclic cellular automata

TLDR
New tools from information theory are introduced that let us calculate the dynamical information content of spatial random processes in CCA, and a complexity measure is introduced to quantitatively determine the rate of self-organization of these cellular automata.

Inferring statistical complexity.

TLDR
A technique is presented that directly reconstructs minimal equations of motion from the recursive structure of measurement sequences, demonstrating a form of superuniversality that refers only to the entropy and complexity of a data stream.

Complexity of two-dimensional patterns

TLDR
A complexity measure based on a mean information gain that does not require knowledge of the “maximal” entropy of the pattern, and at the same time sensitively accounts for the inherent correlations in the system.