What does it mean if the KL divergence between distributions p and q is zero?

What does it mean if the KL divergence between distributions p and q is zero?

1 Answer. This implies that KL divergence is infinite if there exists an x where p(x)>0 and q(x)=0. Conversely, p(x) being zero doesn’t produce infinity, whether or not q(x) is also zero. Another way of saying this is that KL divergence is finite only if the support of p is contained within the support of q.

Is KL divergence smooth?

KL divergence is not Lipschitz smooth because of point (3) : there is a pair of point such that L is unbounded.

How to calculate the KL divergence of a distribution?

With KL divergence we can calculate exactly how much information is lost when we approximate one distribution with another. Let’s go back to our data and see what the results look like. Now we can go ahead and calculate the KL divergence for our two approximating distributions. For the uniform distribution we find:

How does Kullback-Leibler divergence relate to KL divergence?

Kullback-Leibler divergence calculates a score that measures the divergence of one probability distribution from another. Jensen-Shannon divergence extends KL divergence to calculate a symmetrical score and distance measure of one probability distribution from another.

Who is the author of the KL divergence?

Importantly, the KL divergence score is not symmetrical, for example: It is named for the two authors of the method Solomon Kullback and Richard Leibler, and is sometimes referred to as “ relative entropy .” This is known as the relative entropy or Kullback-Leibler divergence, or KL divergence, between the distributions p (x) and q (x).

Is the KL divergence score symmetrical or symmetrical?

Importantly, the KL divergence score is not symmetrical, for example: KL(P || Q) != KL(Q || P) It is named for the two authors of the method Solomon Kullback and Richard Leibler, and is sometimes referred to as “ relative entropy .”