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

TL;DR

This paper introduces a novel structure learning scheme for probabilistic sentential decision diagrams that leverages a partial closed-world assumption, enabling effective modeling of logical constraints and improved generalization.

Contribution

It proposes a new structure learning method for probabilistic sentential decision diagrams based on a partial closed-world assumption, integrating logical constraints into the learning process.

Findings

The approach fits training data well.

It generalizes effectively to test data.

Performance depends on data consistency with the logical base.

Abstract

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.