  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.
