2016/11/04 by Beigi, Salman, Gohari, Amin
#FOS: Computer and information sciences #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.1611.01335
A measure of correlation is said to have the tensorization property if it is unchanged when computed for i.i.d. copies. More precisely, a measure of correlation between two random variables (X, Y) denoted by ρ(X, Y), has the tensorization property if ρ(Xn, Yn)=ρ(X, Y) where (Xn, Yn) is n i.i.d. copies of (X, Y).Two well-known examples of such measures are the maximal correlation and the hypercontractivity ribbon (HC~ribbon). We show that the maximal correlation and HC ribbons are special cases of Φ-ribbon, defined in this paper for any function Φ from a class of convex functions (Φ-ribbon reduces to HC~ribbon and the maximal correlation for special choices of Φ). Any Φ-ribbon is shown to be a measures of correlation with the tensorization property. We show that the Φ-ribbon also characterizes the Φ-strong data processing inequality constant introduced by Raginsky. We further study the Φ-ribbon for the choice of Φ(t)=t2 and introduce an equivalent characterization of this ribbon.