On the Geometry of Maximum Entropy Problems

Details On the Geometry of Maximum Entropy Problems On the Geometry of Maximum Entropy Problems

2011-12-23

arxiv.org/abs/1112.5529v1

Mathematics

Optimization and Control

29 pages

Scientific paper

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.

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