Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential cumulants, hierachical models and monomial ideals   For a joint probability density function f(x) of a random vector X the mixed
partial derivatives of log f(x) can be interpreted as limiting cumulants in an
infinitesimally small open neighborhood around x. Moreover, setting them to
zero everywhere gives independence and conditional independence conditions. The
latter conditions can be mapped, using an algebraic differential duality, into
monomial ideal conditions. This provides an isomorphism between hierarchical
models and monomial ideals. It is thus shown that certain monomial ideals are
associated with particular classes of hierarchical models.

26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat