Approximation Complexity of Maximum A Posteriori Inference in Sum-Product Networks

Diarmaid Conaty, Denis D. Maua, Casio P. de Campos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Citations (Scopus)
100 Downloads (Pure)

Abstract

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 $2^{f(n)}$ for any sublinear function $f$ of the size of the input $n$. Again, this bound is tight, as we prove that the usual max-product algorithm finds (in any network) approximations within factor $2^{c \cdot n}$ for some constant $c < 1$. 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 real-world data.
Original languageEnglish
Title of host publicationProceedings of The 33rd Conference on Uncertainty in Artificial Intelligence
PublisherAUAI
Number of pages10
Publication statusPublished - 01 Aug 2017
EventThe 33rd Conference on Uncertainty in Artificial Intelligence (UAI) - ICC, Sydney, Australia
Duration: 12 Aug 201714 Aug 2017
http://auai.org/uai2017
http://www.auai.org

Conference

ConferenceThe 33rd Conference on Uncertainty in Artificial Intelligence (UAI)
Abbreviated titleUAI
CountryAustralia
CitySydney
Period12/08/201714/08/2017
Internet address

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