Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum KL-divergence on complements of $L_1$ balls   Pinsker's widely used inequality upper-bounds the total variation distance
$||P-Q||_1$ in terms of the Kullback-Leibler divergence $D(P||Q)$. Although in
general a bound in the reverse direction is impossible, in many applications
the quantity of interest is actually $D^*(P,\eps)$ --- defined, for an
arbitrary fixed $P$, as the infimum of $D(P||Q)$ over all distributions $Q$
that are $\eps$-far away from $P$ in total variation. We show that
$D^*(P,\eps)\le C\eps^2 + O(\eps^3)$, where $C=C(P)=1/2$ for "balanced"
distributions, thereby providing a kind of reverse Pinsker inequality. An
application to large deviations is given, and some of the structural results
may be of independent interest. Keywords: Pinsker inequality, Sanov's theorem,
large deviations

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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc