Information inequalities: interpretations & applications

Abstract: We review and refine classical inequalities (of Shannon,  Han, Shearer etc.)
for the joint entropy of a collection of random  variables in terms of an arbitrary
collection of subset joint  entropies. A duality between the upper and new lower bounds
for joint  entropy is developed, as are connections to entropy power  inequalities.
Applications include a new upper bound on the number of  independent sets in an arbitrary
graph, and new determinantal  inequalities. This is current work with Prasad Tetali
(Georgia Tech).