Dec. 20 2005 10:00AM

Dec. 20 2005 10:20AM

For given discrete r-valued distribution a, s-valued distribution b and r×s-valued bivariate distribution q, we study r×s-valued bivariate distributions p with marginals a and b minimizing f-divergences D(p,q). Such distributions p are the least distorted adaptations of distributions q to given marginals a, b when distortions are measured by f-divergences. They are applicable e.g. in transport, artificial inteligence, communication and sociometry. In our research (i) formulas for solutions p are found for all differentiable strictly convex f, (ii) algorithms for recursive approximation of these solutions are proposed for the function f(t) = tlnt leading to the classical information divergence and the function f(t) = t(t-1) leading to the classical chi-squared divergence, and (iii) these algorithms are programmed. The results of our effort will be outlined in the talk and illustrated on concrete sociometric data.

International Workshop on Data - Algorithms - Decision Making (Kontaktní osoba: Martin Janžura)