Abstract: Bayesian networks are probabilistic graphical mod-
els with a wide range of application areas includ-
ing gene regulatory networks inference, risk anal-
ysis and image processing. Learning the structure
of a Bayesian network (BNSL) from discrete data
is known to be an NP-hard task with a superexpo-
nential search space of directed acyclic graphs. In
this work, we propose a new polynomial time algo-
rithm for discovering a subset of all possible cluster
cuts, a greedy algorithm for approximately solving
the resulting linear program, and a generalised arc
consistency algorithm for the acyclicity constraint.
We embed these in the constraint programming-
based branch-and-bound solver CPBayes and show
that, despite being suboptimal, they improve per-
formance by orders of magnitude. The resulting
solver also compares favourably with GOBNILP, a
state-of-the-art solver for the BNSL problem which
solves an NP-hard problem to discover each cut and
solves the linear program exactly.
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