Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Submodular Combinatorial Information Measures with Applications in
  Machine Learning   Information-theoretic quantities like entropy and mutual information have
found numerous uses in machine learning. It is well known that there is a
strong connection between these entropic quantities and submodularity since
entropy over a set of random variables is submodular. In this paper, we study
combinatorial information measures that generalize independence, (conditional)
entropy, (conditional) mutual information, and total correlation defined over
sets of (not necessarily random) variables. These measures strictly generalize
the corresponding entropic measures since they are all parameterized via
submodular functions that themselves strictly generalize entropy. Critically,
we show that, unlike entropic mutual information in general, the submodular
mutual information is actually submodular in one argument, holding the other
fixed, for a large class of submodular functions whose third-order partial
derivatives satisfy a non-negativity property. This turns out to include a
number of practically useful cases such as the facility location and set-cover
functions. We study specific instantiations of the submodular information
measures on these, as well as the probabilistic coverage, graph-cut, and
saturated coverage functions, and see that they all have mathematically
intuitive and practically useful expressions. Regarding applications, we
connect the maximization of submodular (conditional) mutual information to
problems such as mutual-information-based, query-based, and privacy-preserving
summarization -- and we connect optimizing the multi-set submodular mutual
information to clustering and robust partitioning.

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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics