Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimating R\'enyi's $\alpha$-Cross-Entropies in a Matrix-Based Way   Conventional information-theoretic quantities assume access to probability
distributions. Estimating such distributions is not trivial. Here, we consider
function-based formulations of cross entropy that sidesteps this a priori
estimation requirement. We propose three measures of R\'enyi's
$\alpha$-cross-entropies in the setting of reproducing-kernel Hilbert spaces.
Each measure has its appeals. We prove that we can estimate these measures in
an unbiased, non-parametric, and minimax-optimal way. We do this via
sample-constructed Gram matrices. This yields matrix-based estimators of
R\'enyi's $\alpha$-cross-entropies. These estimators satisfy all of the axioms
that R\'enyi established for divergences. Our cross-entropies can thus be used
for assessing distributional differences. They are also appropriate for
handling high-dimensional distributions, since the convergence rate of our
estimator is independent of the sample dimensionality.
  Python code for implementing these measures can be found at
https://github.com/isledge/MBRCE

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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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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: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: stat