Probabilistic Generating Circuits

About

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.

Honghua Zhang, Brendan Juba, Guy Van den Broeck · 2021

Related benchmarks

Task	Dataset	Result
Density Estimation	MSWeb Twenty Datasets (test)	Log-Likelihood-10.14	8
Density Estimation	book discrete (test)	Log-Likelihood-34.84	7
Density Estimation	msnbc discrete (test)	Log-Likelihood-6.04	7
Density Estimation	Kosarek Twenty Datasets (test)	Log-LH-10.88	4
Density Estimation	Plants Twenty Datasets (test)	Log-Likelihood-13.41	4
Density Estimation	Retail Twenty Datasets (test)	Log-Likelihood-10.9	4
Density Estimation	Pumsb-star Twenty Datasets (test)	Log-Likelihood-31.08	4
Density Estimation	EachMovie Twenty Datasets (test)	Log-Likelihood-52.85	4
Density Estimation	NLTCS Twenty Datasets (test)	Log-Likelihood-6.02	4
Density Estimation	KDDCup2k Twenty Datasets (test)	Log-Likelihood-2.14	4