Technical Program

Paper Detail

Paper Title Unifying the Brascamp-Lieb Inequality and the Entropy Power Inequality
Paper IdentifierTH1.R5.3
Authors Venkat Anantharam, University of California, Berkeley, United States; Varun Jog, University of Wisconsin - Madison, United States; Chandra Nair, The Chinese University of Hong Kong, Hong Kong SAR of China
Session Extremal Distributions
Location Saint Victor, Level 3
Session Time Thursday, 11 July, 09:50 - 11:10
Presentation Time Thursday, 11 July, 10:30 - 10:50
Manuscript  Click here to download the manuscript
Abstract The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors. The EPI provides lower bounds for the differential entropy of linear transformations of random vectors with independent components. The BLI, on the other hand, provides upper bounds on the differential entropy of a random vector in terms of the differential entropies of some of its linear transformations. In this paper, we define a family of entropy functionals, which we show are subadditive. We then establish that Gaussians are extremal for these functionals by mimicking the idea in Geng and Nair (2014). As a consequence, we obtain a new entropy inequality that generalizes both the BLI and EPI. By considering a variety of independence relations among the components of the random vectors appearing in these functionals, we also obtain families of inequalities that lie between the EPI and the BLI.