Exact Maximum-Entropy Estimation with Feynman Diagrams

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Pages (from-to)731-747
Number of pages17
JournalJournal of Statistical Physics
Issue number4
StatePublished - 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.


  • Feynman calculus
  • Maximum entropy
  • Perturbative expansion
  • Weighted trees


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