Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measures of Entropy from Data Using Infinitely Divisible Kernels   Information theory provides principled ways to analyze different inference
and learning problems such as hypothesis testing, clustering, dimensionality
reduction, classification, among others. However, the use of information
theoretic quantities as test statistics, that is, as quantities obtained from
empirical data, poses a challenging estimation problem that often leads to
strong simplifications such as Gaussian models, or the use of plug in density
estimators that are restricted to certain representation of the data. In this
paper, a framework to non-parametrically obtain measures of entropy directly
from data using operators in reproducing kernel Hilbert spaces defined by
infinitely divisible kernels is presented. The entropy functionals, which bear
resemblance with quantum entropies, are defined on positive definite matrices
and satisfy similar axioms to those of Renyi's definition of entropy.
Convergence of the proposed estimators follows from concentration results on
the difference between the ordered spectrum of the Gram matrices and the
integral operators associated to the population quantities. In this way,
capitalizing on both the axiomatic definition of entropy and on the
representation power of positive definite kernels, the proposed measure of
entropy avoids the estimation of the probability distribution underlying the
data. Moreover, estimators of kernel-based conditional entropy and mutual
information are also defined. Numerical experiments on independence tests
compare favourably with state of the art.

35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys