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2 votes
1 answer
115 views

Reference request for elementary convex geometry property

I need to use the following lemma for a proof. It is an elementary result, which I am sure is well known, just I am not familiar enough with the relative literature to find a direct reference. Is ther …
8 votes
1 answer
685 views

Is the square root of the Kullback-Leibler divergence a convex map?

$\newcommand{\KL}{\operatorname{KL}}$Let $X$ be a Polish metric space and $P(X)$ the space of probability measures on $X$. Given $\mu, \nu\in P(X)$, recall that $$\KL(\mu\parallel\nu) = \begin{cases}\ …