What is the cross entropy between the continuous conditional probability $ p(z|x) $ and the probability $r(z)$?
Should it be:
$$ CH(p(z|x),r(z))=-\int\int p(z|x)log\left(r(z)\right)dxdz $$
Or:
$$ CH(p(z|x),r(z))=-\int\int p(z,x)log\left(r(z)\right)dxdz $$
Or maybe something else?
Thanks!!