Sparse Probabilistic Graph Circuits

TL;DR

This paper introduces Sparse Probabilistic Graph Circuits (SPGCs), a scalable, tractable generative model for sparse graphs that improves inference efficiency and retains high performance in drug design applications.

Contribution

We propose Sparse PGCs that operate on sparse graph representations, reducing complexity from quadratic to linear in nodes and edges, enabling scalable probabilistic inference.

Findings

SPGCs retain exact inference capabilities.

SPGCs improve memory efficiency and inference speed.

SPGCs match the performance of intractable DGMs in drug design metrics.

Abstract

Deep generative models (DGMs) for graphs achieve impressively high expressive power thanks to very efficient and scalable neural networks. However, these networks contain non-linearities that prevent analytical computation of many standard probabilistic inference queries, i.e., these DGMs are considered \emph{intractable}. While recently proposed Probabilistic Graph Circuits (PGCs) address this issue by enabling \emph{tractable} probabilistic inference, they operate on dense graph representations with $\mathcal{O}(n^2)$ complexity for graphs with $n$ nodes and \emph{$m$ edges}. To address this scalability issue, we introduce Sparse PGCs, a new class of tractable generative models that operate directly on sparse graph representation, reducing the complexity to $\mathcal{O}(n + m)$, which is particularly beneficial for $m \ll n^2$. In the context of de novo drug design, we empirically demonstrate that SPGCs retain exact inference capabilities, improve memory efficiency and inference speed, and match the performance of intractable DGMs in key metrics.