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Is there a maximum (unique?) to the KL divergence between discrete distributions p & q, with the restriction that q is a proper probability distribution?

I know KL is unbounded from above when q is unrestricted, but what about when it sums to one?

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    $\begingroup$ AFAIK the definition of KL divergence assumes that $q$ is a proper probability distribution, so I don't think you are adding a meaningful restriction. $\endgroup$
    – leonbloy
    May 4, 2019 at 12:55

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