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Probabilistic sentential decision diagrams are a class ofstructured-decomposable probabilistic circuits especially designed to embedlogical constraints. To adapt the classical LearnSPN scheme to learn thestructure of these models, we propose a new scheme based on a partialclosed-world assumption: data implicitly provide the logical base of thecircuit. Sum nodes are thus learned by recursively clustering batches in theinitial data base, while the partitioning of the variables obeys a given inputvtree. Preliminary experiments show that the proposed approach might properlyfit training data, and generalize well to test data, provided that these remainconsistent with the underlying logical base, that is a relaxation of thetraining data base.

Structural Learning of Probabilistic Sentential Decision Diagrams under Partial Closed-World Assumption