Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences

2026-03-20

AI Summary

This work addresses the challenge in adversarial learning when the target distribution conforms to a known Bayesian network structure, where conventional graph-agnostic GANs fail to exploit structural information, leading to unstable training and poor structure recovery. To overcome this, the authors propose a graph-guided adversarial modeling approach that constructs a structure-aware discriminator by decomposing the global variational divergence into a mean of local family-wise divergences aligned with the graph topology. Leveraging (f,Γ)-divergence, integral probability metrics, and proximal optimal transport, they design a class of local discriminators and establish a graph-informed adversarial training framework. Theoretically, they prove the subadditivity of the infimum of interpolated divergences, providing a variational justification for replacing the global discriminator with local counterparts. Experiments demonstrate that the proposed method significantly enhances training stability and the ability to recover the underlying graphical structure.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We study adversarial learning when the target distribution factorizes according to a known Bayesian network. For interpolative divergences, including $(f,Γ)$-divergences, we prove a new infimal subadditivity principle showing that, under suitable conditions, a global variational discrepancy is controlled by an average of family-level discrepancies aligned with the graph. In an additive regime, this surrogate is exact. 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. The result does not require the optimizer itself to factorize according to the graph. We also obtain parallel results for integral probability metrics and proximal optimal transport divergences, identify natural discriminator classes for which the theory applies, and present experiments showing improved stability and structural recovery relative to graph-agnostic baselines.

Problem

• adversarial learning
• Bayesian network
• graph-informed modeling
• structured distributions
• generative adversarial networks

Innovation

• graph-informed GAN
• infimal subadditivity
• interpolative divergences
• Bayesian network
• localized discriminators