I understand that KL divergence between two distributions is only defined when the two distributions are defined on the exact same probability space. This means that one cannot straight up compute KL divergence between a discrete and a continuous distribution.
However, is there a handy (or well-understood) way of computing the KL divergence between a Poisson and a Normal distribution?
I would generally think of discretizing the continuous distribution and then numerically computing the KL divergence between the two. But I'm wondering for the specific case of Poisson and Normal, if there's a clean way to do that.