  Probabilistic sentential decision diagrams are a class of
structured-decomposable probabilistic circuits especially designed to embed
logical constraints. To adapt the classical LearnSPN scheme to learn the
structure of these models, we propose a new scheme based on a partial
closed-world assumption: data implicitly provide the logical base of the
circuit. Sum nodes are thus learned by recursively clustering batches in the
initial data base, while the partitioning of the variables obeys a given input
vtree. Preliminary experiments show that the proposed approach might properly
fit training data, and generalize well to test data, provided that these remain
consistent with the underlying logical base, that is a relaxation of the
training data base.

Artificial Intelligence