Journal of Statistical Physics

, Volume 170, Issue 4, pp 731–747 | Cite as

Exact Maximum-Entropy Estimation with Feynman Diagrams

  • Amitai Netser Zernik
  • Tomer M. Schlank
  • Ran J. Tessler
Article
  • 33 Downloads

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.

Keywords

Feynman calculus Maximum entropy Perturbative expansion Weighted trees 

Notes

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.

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Amitai Netser Zernik
    • 1
  • Tomer M. Schlank
    • 2
  • Ran J. Tessler
    • 3
  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  3. 3.Institute for Theoretical StudiesETH ZürichZurichSwitzerland

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