Suppose we are given a discrete probability distribution $p$ defined over a finite set $\mathcal{S}$. We have $p(s) > 0, \forall s\in\mathcal{S}$. Suppose we now want to find the distribution $q$ that maximizes the KL-divergence $D(p||q)$ between $p$ and $q$, subject to the constraint that $q(s) > 0, \forall s\in\mathcal{S}$. What would be such a distribution?
2026-03-31 19:18:11.1774984691
Maximum KL-divergence between two discrete distributions with non-zero mass on each point of support.
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