On the Relationship Between Probabilistic Circuits and Determinantal Point Processes

TL;DR

This paper explores the relationship between determinantal point processes and probabilistic circuits, providing a unified analysis, revealing theoretical barriers, and discussing the challenges in unifying these tractable probabilistic models.

Contribution

It offers the first systematic analysis of DPPs and PCs, establishing theoretical limitations and proposing a shared framework for understanding both classes of models.

Findings

DPPs and PCs have distinct structural properties.

There are cases where DPPs cannot be represented as PCs.

The paper highlights fundamental barriers to unifying these models.

Abstract

Scaling probabilistic models to large realistic problems and datasets is a key challenge in machine learning. Central to this effort is the development of tractable probabilistic models (TPMs): models whose structure guarantees efficient probabilistic inference algorithms. The current landscape of TPMs is fragmented: there exist various kinds of TPMs with different strengths and weaknesses. Two of the most prominent classes of TPMs are determinantal point processes (DPPs) and probabilistic circuits (PCs). This paper provides the first systematic study of their relationship. We propose a unified analysis and shared language for discussing DPPs and PCs. Then we establish theoretical barriers for the unification of these two families, and prove that there are cases where DPPs have no compact representation as a class of PCs. We close with a perspective on the central problem of unifying these tractable models.