Beyond Inverse Ising Model: Structure of the Analytical Solution View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2013-02

AUTHORS

Iacopo Mastromatteo

ABSTRACT

I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the entropy of a system as a function of its corresponding observables, I show the conditions under which this can be done without resorting to iterative algorithms. I find that inverse problems are local (the inverse Fisher information is sparse) whenever the corresponding models have a factorized form, and the entropy can be split in a sum of small cluster contributions. I illustrate these ideas through two examples (the Ising model on a tree and the one-dimensional periodic chain with arbitrary order interaction) and support the results with numerical simulations. The extension of these methods to more general scenarios is finally discussed. More... »

PAGES

658-670

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-013-0707-y

DOI

http://dx.doi.org/10.1007/s10955-013-0707-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1027584372


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