TITLE: Can I normalize KL-divergence to be $\leq 1$?
QUESTION [14 upvotes]: The Kullback-Leibler divergence has a strong relationship with mutual information, and mutual information has a number of normalized variants.  Is there some similar, entropy-like value that I can use to normalize KL-divergence such that the normalized KL-divergence is bounded above by 1 (and below by 0)?

REPLY [2 votes]: The KL is only defined for distributions having compatible supports... Nevertheless, it is true that one can find distributions that have infinite KL divergence.