Mixed f-divergence and inequalities for log-concave functions Article

Caglar, U, Werner, EM. (2012). Mixed f-divergence and inequalities for log-concave functions . PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 110(2), 271-290. 10.1112/plms/pdu055

cited authors

  • Caglar, U; Werner, EM

authors

abstract

  • Mixed f-divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log-concave functions and establish some of their properties. Among them are affine invariant vector entropy inequalities, like new Alexandrov-Fenchel-type inequalities and an affine isoperimetric inequality for the vector form of the Kullback Leibler divergence for log-concave functions. Special cases of f-divergences are mixed L-╬╗-affine surface areas for log-concave functions. For those, we establish various affine isoperimetric inequalities as well as a vector Blaschke Santal├│-type inequality.

publication date

  • December 18, 2012

Digital Object Identifier (DOI)

start page

  • 271

end page

  • 290

volume

  • 110

issue

  • 2