Graph-informed GANs: Variational learning with Bayesian network structure

Description

ABSTRACT. We study adversarial learning when the target distribution factorizes according to a known Bayesian network. Our focus is on interpolative divergences, such as $(f,\Gamma)$-divergences, which connect classical $f$-divergences and integral probability metrics through variational objectives with constrained discriminator classes. We establish a new \emph{infimal subadditivity} principle showing that, under suitable conditions, a graph-constrained global objective is bounded by an average of family-level objectives on the local neighborhoods of the graph, with equality in an additive regime. This provides a variational justification for replacing a graph-agnostic GAN with a monolithic discriminator by a graph-informed GAN with localized family-level discriminators. We also establish parallel results for integral probability metrics and proximal optimal transport divergences, and present numerical experiments illustrating improved stability and structural recovery in graph-informed training.

Period	3 Jul 2026
Event title	Scientific Computing and Differential Equations (SciCADE) 2026
Event type	Conference
Location	Edinburgh, United KingdomShow on map
Degree of Recognition	International