Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $k$-NN Estimation of Directed Information   This report studies data-driven estimation of the directed information (DI)
measure between two{em discrete-time and continuous-amplitude} random process,
based on the $k$-nearest-neighbors ($k$-NN) estimation framework. Detailed
derivations of two $k$-NN estimators are provided. The two estimators differ in
the metric based on which the nearest-neighbors are found. To facilitate the
estimation of the DI measure, it is assumed that the observed sequences are
(jointly) Markovian of order $m$. As $m$ is generally not known, a data-driven
method (that is also based on the $k$-NN principle) for estimating $m$ from the
observed sequences is presented. An exhaustive numerical study shows that the
discussed $k$-NN estimators perform well even for relatively small number of
samples (few thousands). Moreover, it is shown that the discussed estimators
are capable of accurately detecting linear as well as non-linear causal
interactions.

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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
18
The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat