Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms and Complexity Results for Exact Bayesian Structure Learning   Bayesian structure learning is the NP-hard problem of discovering a Bayesian
network that optimally represents a given set of training data. In this paper
we study the computational worst-case complexity of exact Bayesian structure
learning under graph theoretic restrictions on the super-structure. The
super-structure (a concept introduced by Perrier, Imoto, and Miyano, JMLR 2008)
is an undirected graph that contains as subgraphs the skeletons of solution
networks. Our results apply to several variants of score-based Bayesian
structure learning where the score of a network decomposes into local scores of
its nodes. Results: We show that exact Bayesian structure learning can be
carried out in non-uniform polynomial time if the super-structure has bounded
treewidth and in linear time if in addition the super-structure has bounded
maximum degree. We complement this with a number of hardness results. We show
that both restrictions (treewidth and degree) are essential and cannot be
dropped without loosing uniform polynomial time tractability (subject to a
complexity-theoretic assumption). Furthermore, we show that the restrictions
remain essential if we do not search for a globally optimal network but we aim
to improve a given network by means of at most k arc additions, arc deletions,
or arc reversals (k-neighborhood local search).

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The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: adap-org
2
The categories of this paper are: math
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an