Exact Maximum-Entropy Estimation with Feynman Diagrams

Amitai Netser Zernik; Tomer M. Schlank; Ran J. Tessler

doi:10.1007/s10955-018-1960-x

Exact Maximum-Entropy Estimation with Feynman Diagrams

Amitai Netser Zernik, Tomer M. Schlank, Ran J. Tessler^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	American English
Pages (from-to)	731-747
Number of pages	17
Journal	Journal of Statistical Physics
Volume	170
Issue number	4
DOIs	https://doi.org/10.1007/s10955-018-1960-x
State	Published - 1 Feb 2018

Bibliographical note

Funding Information:
Acknowledgements We thank O. Bozo, B. Gomberg, R.S. Melzer, A. Moscovitch-Eiger, R. Schweiger, A. Solomon and D. Zernik for discussions related to the work presented here. R.T. was partially supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation.

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Feynman calculus
Maximum entropy
Perturbative expansion
Weighted trees

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10.1007/s10955-018-1960-x

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title = "Exact Maximum-Entropy Estimation with Feynman Diagrams",

abstract = "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.",

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Exact Maximum-Entropy Estimation with Feynman Diagrams

Abstract

Bibliographical note

Keywords

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