Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Trek separation for Gaussian graphical models   Gaussian graphical models are semi-algebraic subsets of the cone of positive
definite covariance matrices. Submatrices with low rank correspond to
generalizations of conditional independence constraints on collections of
random variables. We give a precise graph-theoretic characterization of when
submatrices of the covariance matrix have small rank for a general class of
mixed graphs that includes directed acyclic and undirected graphs as special
cases. Our new trek separation criterion generalizes the familiar
$d$-separation criterion. Proofs are based on the trek rule, the resulting
matrix factorizations and classical theorems of algebraic combinatorics on the
expansions of determinants of path polynomials.

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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci