Exact Maximum-Entropy Estimation with Feynman Diagrams

A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over we...

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Veröffentlicht in:	Journal of statistical physics 2018-02, Vol.170 (4), p.731-747
Hauptverfasser:	Netser Zernik, Amitai, Schlank, Tomer M., Tessler, Ran J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Calculus CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ENTROPY FEYNMAN DIAGRAM Feynman diagrams LIMITING VALUES Mathematical and Computational Physics MATHEMATICAL SOLUTIONS PERTURBATION THEORY Physical Chemistry Physics Physics and Astronomy PROBABILITY Quantum Physics Statistical Physics and Dynamical Systems STATISTICS Theoretical WEIGHTING FUNCTIONS
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Beschreibung
Zusammenfassung:	A longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using perturbative Feynman calculus. The explicit expression is given as a sum over weighted trees.
ISSN:	0022-4715 1572-9613
DOI:	10.1007/s10955-018-1960-x