Conditional entropic Ruzsa distance
= Conditional entropic Ruzsa distance
{c}
{title2=$d_R(X\mid U;Y\mid V)$}
For finitely supported random variables, the conditional entropic Ruzsa distance is
$$
d_R(X\mid U;Y\mid V)
=\sum_{u,v}\mathbb P(U=u)\mathbb P(V=v)
d_R(X\mid U=u,Y\mid V=v).
$$
Thus the two conditioning values are sampled independently. If only one variable is conditioned, write $d_R(X\mid U;Y)$.