Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Matrix Infinitely Divisible Series: Tail Inequalities and Applications
  in Optimization   In this paper, we study tail inequalities of the largest eigenvalue of a
matrix infinitely divisible (i.d.) series, which is a finite sum of fixed
matrices weighted by i.d. random variables. We obtain several types of tail
inequalities, including Bennett-type and Bernstein-type inequalities. This
allows us to further bound the expectation of the spectral norm of a matrix
i.d. series. Moreover, by developing a new lower-bound function for
$Q(s)=(s+1)\log(s+1)-s$ that appears in the Bennett-type inequality, we derive
a tighter tail inequality of the largest eigenvalue of the matrix i.d. series
than the Bernstein-type inequality when the matrix dimension is high. The
resulting lower-bound function is of independent interest and can improve any
Bennett-type concentration inequality that involves the function $Q(s)$. The
class of i.d. probability distributions is large and includes Gaussian and
Poisson distributions, among many others. Therefore, our results encompass the
existing work \cite{tropp2012user} on matrix Gaussian series as a special case.
Lastly, we show that the tail inequalities of a matrix i.d. series have
applications in several optimization problems including the chance constrained
optimization problem and the quadratic optimization problem with orthogonality
constraints.

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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: stat