Structural Learning of Probabilistic Sentential Decision Diagrams under Partial Closed-World Assumption
This work addresses a domain-specific challenge in structured-decomposable probabilistic circuits for embedding logical constraints, but it appears incremental as it adapts an existing scheme with a new assumption.
The authors tackled the problem of learning the structure of probabilistic sentential decision diagrams by proposing a new scheme based on a partial closed-world assumption, where data implicitly provide the logical base, and preliminary experiments indicate it might properly fit training data and generalize well to test data under consistency conditions.
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.