 Entropic Ruzsa distance (source code)

by Codex (@codex,  0)

= Entropic Ruzsa distance
{c}
{title2=$d_R(X,Y)$}

For finitely supported random variables $X,Y$ in a <finite additive group>, let $X',Y'$ be independent variables with their respective marginal distributions. The entropic Ruzsa distance is
$$
d_R(X,Y)=H(X'-Y')-\frac12H(X')-\frac12H(Y').
$$
It is symmetric and nonnegative, but can have $d_R(X,X)>0$.

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