17,835 research outputs found
Advances in Learning Bayesian Networks of Bounded Treewidth
This work presents novel algorithms for learning Bayesian network structures
with bounded treewidth. Both exact and approximate methods are developed. The
exact method combines mixed-integer linear programming formulations for
structure learning and treewidth computation. The approximate method consists
in uniformly sampling -trees (maximal graphs of treewidth ), and
subsequently selecting, exactly or approximately, the best structure whose
moral graph is a subgraph of that -tree. Some properties of these methods
are discussed and proven. The approaches are empirically compared to each other
and to a state-of-the-art method for learning bounded treewidth structures on a
collection of public data sets with up to 100 variables. The experiments show
that our exact algorithm outperforms the state of the art, and that the
approximate approach is fairly accurate.Comment: 23 pages, 2 figures, 3 table
Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks
We discuss the computational complexity of approximating maximum a posteriori
inference in sum-product networks. We first show NP-hardness in trees of height
two by a reduction from maximum independent set; this implies
non-approximability within a sublinear factor. We show that this is a tight
bound, as we can find an approximation within a linear factor in networks of
height two. We then show that, in trees of height three, it is NP-hard to
approximate the problem within a factor for any sublinear function
of the size of the input . Again, this bound is tight, as we prove that
the usual max-product algorithm finds (in any network) approximations within
factor for some constant . Last, we present a simple
algorithm, and show that it provably produces solutions at least as good as,
and potentially much better than, the max-product algorithm. We empirically
analyze the proposed algorithm against max-product using synthetic and
realistic networks.Comment: 18 page
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