Finding the maximizers of the information divergence from an exponential family
J Rauh - IEEE transactions on information theory, 2011 - ieeexplore.ieee.org
IEEE transactions on information theory, 2011•ieeexplore.ieee.org
This paper investigates maximizers of the information divergence from an exponential family
\calE. It is shown that the rI-projection of a maximizer P to \calE is a convex combination of P
and a probability measure P_- with disjoint support and the same value of the sufficient
statistics A. This observation can be used to transform the original problem of maximizing
D(⋅‖\calE) over the set of all probability measures into the maximization of a function
\overlineD_r over a convex subset of \kerA. The global maximizers of both problems …
\calE. It is shown that the rI-projection of a maximizer P to \calE is a convex combination of P
and a probability measure P_- with disjoint support and the same value of the sufficient
statistics A. This observation can be used to transform the original problem of maximizing
D(⋅‖\calE) over the set of all probability measures into the maximization of a function
\overlineD_r over a convex subset of \kerA. The global maximizers of both problems …
This paper investigates maximizers of the information divergence from an exponential family . It is shown that the -projection of a maximizer to is a convex combination of and a probability measure with disjoint support and the same value of the sufficient statistics . This observation can be used to transform the original problem of maximizing over the set of all probability measures into the maximization of a function over a convex subset of . The global maximizers of both problems correspond to each other. Furthermore, finding all local maximizers of yields all local maximizers of .
ieeexplore.ieee.org