On the geometry of maximum entropy problems

Michele Pavon, Augusto Ferrante

Research output: Contribution to journalReview articlepeer-review


We show that a simple geometric result suffices to derive the form of the optimal solution in a large class of finite- and infinite-dimensional maximum entropy problems concerning probability distributions, spectral densities, and covariance matrices. These include Burg's spectral estimation method and Dempster's covariance completion, as well as various recent generalizations of the above. We then apply this orthogonality principle to the new problem of completing a block-circulant covariance matrix when an a priori estimate is available.

Original languageEnglish (US)
Pages (from-to)415-419
Number of pages5
JournalSIAM Review
Issue number3
StatePublished - 2013


  • Covariance selection
  • Geometric principle
  • Gibbs's variational principle
  • Maximum entropy problem
  • Spectral estimation

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics


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