2013/02/02 by Adityanand Guntuboyina, Guntuboyina, Adityanand, Sujayam Saha +3
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Probability (math.PR) #Statistics Theory (math.ST) #cs.IT #math.IT #math.OC #math.PR #math.ST #stat.ML #stat.TH
paper · pdf · doi:10.48550/arxiv.1302.0336
arxiv created 2013/10/15 · arxiv updated 2013/10/16
f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an f-divergence between two probability measures subject to a finite number of constraints on other f-divergences. We show that these infinite-dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable. Our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between f-divergences. We demonstrate that many of the existing results on inequalities between f-divergences can be obtained as special cases of our results and we also improve on some existing non-sharp inequalities.