  Probabilistic circuits (PCs) are a powerful modeling framework for
representing tractable probability distributions over combinatorial spaces. In
machine learning and probabilistic programming, one is often interested in
understanding whether the distributions learned using PCs are close to the
desired distribution. Thus, given two probabilistic circuits, a fundamental
problem of interest is to determine whether their distributions are close to
each other.
  The primary contribution of this paper is a closeness test for PCs with
respect to the total variation distance metric. Our algorithm utilizes two
common PC queries, counting and sampling. In particular, we provide a poly-time
probabilistic algorithm to check the closeness of two PCs when the PCs support
tractable approximate counting and sampling. We demonstrate the practical
efficiency of our algorithmic framework via a detailed experimental evaluation
of a prototype implementation against a set of 475 PC benchmarks. We find that
our test correctly decides the closeness of all 475 PCs within 3600 seconds.
