Due to legal requirements like the European General Data Protection Regulation (GDPR), the California Consumer Privacy Act, and many others, users gain more control over their personal data collected daily. The right to be forgotten is of particular importance, which states that collected data must be deleted when requested. Deleting data is often insufficient to provide real data privacy. This is especially the case if the data was used to train machine learning models since they might expose information about their training data via white-box or even black-box access. Motivated by this, the field of Machine Unlearning and Forgetting gained more and more attention.

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.