Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum Rates of Approximate Sufficient Statistics   Given a sufficient statistic for a parametric family of distributions, one
can estimate the parameter without access to the data. However, the memory or
code size for storing the sufficient statistic may nonetheless still be
prohibitive. Indeed, for $n$ independent samples drawn from a $k$-nomial
distribution with $d=k-1$ degrees of freedom, the length of the code scales as
$d\log n+O(1)$. In many applications, we may not have a useful notion of
sufficient statistics (e.g., when the parametric family is not an exponential
family) and we also may not need to reconstruct the generating distribution
exactly. By adopting a Shannon-theoretic approach in which we allow a small
error in estimating the generating distribution, we construct various {\em
approximate sufficient statistics} and show that the code length can be reduced
to $\frac{d}{2}\log n+O(1)$. We consider errors measured according to the
relative entropy and variational distance criteria. For the code constructions,
we leverage Rissanen's minimum description length principle, which yields a
non-vanishing error measured according to the relative entropy. For the
converse parts, we use Clarke and Barron's formula for the relative entropy of
a parametrized distribution and the corresponding mixture distribution.
However, this method only yields a weak converse for the variational distance.
We develop new techniques to achieve vanishing errors and we also prove strong
converses. The latter means that even if the code is allowed to have a
non-vanishing error, its length must still be at least $\frac{d}{2}\log n$.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg