GraphSPNs: Sum-Product Networks Benefit From Canonical Orderings

TL;DR

GraphSPNs are a new deep generative model for graphs that enable exact, efficient inference and can generate valid molecular graphs, outperforming some existing intractable models.

Contribution

Introduction of GraphSPNs, a tractable deep generative model for graphs that ensures permutation invariance through canonical ordering.

Findings

GraphSPNs achieve exact inference on graphs.

They can generate chemically valid molecular graphs.

GraphSPNs outperform some existing models in graph generation.

Abstract

Deep generative models have recently made a remarkable progress in capturing complex probability distributions over graphs. However, they are intractable and thus unable to answer even the most basic probabilistic inference queries without resorting to approximations. Therefore, we propose graph sum-product networks (GraphSPNs), a tractable deep generative model which provides exact and efficient inference over (arbitrary parts of) graphs. We investigate different principles to make SPNs permutation invariant. We demonstrate that GraphSPNs are able to (conditionally) generate novel and chemically valid molecular graphs, being competitive to, and sometimes even better than, existing intractable models. We find out that (Graph)SPNs benefit from ensuring the permutation invariance via canonical ordering.