On the Geometry of Maximum Entropy Problems

Giovedi' 23 Febbraio 2012 - Michele Pavon


Giovedi' 23 Febbraio 2012, alle 12:00 in aula 1AD100, il Prof. Michele Pavon terra' un seminario dal titolo "On the Geometry of Maximum Entropy Problems".

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. This orthogonality principle is then applied to the new problem of completing a block-circulant covariance matrix when an a priori estimate is available.

Rif. int. P. Dai Pra