Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension-Free Empirical Entropy Estimation   We seek an entropy estimator for discrete distributions with fully empirical
accuracy bounds. As stated, this goal is infeasible without some prior
assumptions on the distribution. We discover that a certain information moment
assumption renders the problem feasible. We argue that the moment assumption is
natural and, in some sense, {\em minimalistic} -- weaker than finite support or
tail decay conditions. Under the moment assumption, we provide the first
finite-sample entropy estimates for infinite alphabets, nearly recovering the
known minimax rates. Moreover, we demonstrate that our empirical bounds are
significantly sharper than the state-of-the-art bounds, for various natural
distributions and non-trivial sample regimes. Along the way, we give a
dimension-free analogue of the Cover-Thomas result on entropy continuity (with
respect to total variation distance) for finite alphabets, which may be of
independent interest. Additionally, we resolve all of the open problems posed
by J\"urgensen and Matthews, 2010.

36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ