Bayesian network learning by compiling to weighted MAX-SAT

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


The problem of learning discrete Bayesian networks from data is encoded as a weighted MAX-SAT problem and the MaxWalkSat local search algorithm is used to address it. For each dataset, the per-variable summands of the (BDeu) marginal likelihood for different choices of parents (?family scores?) are computed prior to applying MaxWalkSat. Each permissible choice of parents for each variable is encoded as a distinct propositional atom and the associated family score encoded as a ?soft? weighted single-literal clause. Two approaches to enforcing acyclicity are considered: either by encoding the ancestor relation or by attaching a total order to each graph and encoding that. The latter approach gives better results. Learning experiments have been conducted on 21 synthetic datasets sampled from 7 BNs. The largest dataset has 10,000 datapoints and 60 variables producing (for the ?ancestor? encoding) a weighted CNF input file with 19,932 atoms and 269,367 clauses. For most datasets, MaxWalkSat quickly finds BNs with higher BDeu score than the ?true? BN. The effect of adding prior information is assessed. It is further shown that Bayesian model averaging can be effected by collecting BNs generated during the search.
Original languageEnglish
Title of host publicationProceedings of the 24th Conference on Uncertainty in Artificial Intelligence (UAI 2008)
EditorsDavid McAllester, Petri Myllymaki
Place of PublicationCorvallis, Oregon
PublisherAUAI Press
Number of pages8
ISBN (Print)0-9749039-4-9
Publication statusPublished - 2008
Event24th Conference on Uncertainty in Artificial Intelligence - Helsinki, Finland
Duration: 9 Jul 200812 Jul 2008


Conference24th Conference on Uncertainty in Artificial Intelligence

Cite this