Probabilistic Generating Circuits
This work addresses the need for more expressive and efficient probabilistic models in machine learning, offering a novel framework that could impact various applications, though it appears incremental in building upon existing concepts.
The paper tackles the problem of creating a tractable probabilistic model by proposing probabilistic generating circuits (PGCs), which unify and are more expressive than existing models like determinantal point processes and probabilistic circuits, achieving competitive performance on density estimation benchmarks.
Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.