Name
Abstract | ||
|---|---|---|
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 $\rho(X, Y)$, has the tensorization property if $\rho(X^n, Y^n)=\rho(X, Y)$ where $(X^n, Y^n)$ 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 $\Phi$-ribbon, defined in this paper for any function $\Phi$ from a class of convex functions ($\Phi$-ribbon reduces to HC~ribbon and the maximal correlation for special choices of $\Phi$). Any $\Phi$-ribbon is shown to be a measures of correlation with the tensorization property. We show that the $\Phi$-ribbon also characterizes the $\Phi$-strong data processing inequality constant introduced by Raginsky. We further study the $\Phi$-ribbon for the choice of $\Phi(t)=t^2$ and introduce an equivalent characterization of this ribbon. |
Year | Venue | DocType |
|---|---|---|
2016 | CoRR | Journal |
Volume | Citations | PageRank |
abs/1611.01335 | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Salman Beigi | 1 | 56 | 11.43 |
| Amin Gohari | 2 | 144 | 21.81 |