Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors

TL;DR

This paper identifies limitations of Bayesian latent space models for graphs under misspecification and proposes a generalized posterior approach with a new method to improve inference calibration and geometry selection.

Contribution

It introduces a generalized posterior framework and Link-Sequential R-SafeBayes method to enhance robustness and model selection in Bayesian latent space graph models.

Findings

Improved calibration of Bayesian inference under misspecification.

Enhanced link prediction performance on synthetic and real networks.

Reliable criterion for selecting latent geometries across different spaces.

Abstract

Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and structural anomalies that break standard metric properties. We show that such misspecification pushes the data-generating distribution outside the model class, causing Bayesian inference to become overconfident and poorly calibrated. To address this, we propose a generalized posterior framework for random geometric graphs. We introduce Link-Sequential R-SafeBayes, a method that exploits dyadic conditional independence to estimate prequential risk and adaptively tune posterior regularization. Experiments on synthetic and real-world networks demonstrate improved calibration, better link prediction performance, and a reliable criterion for selecting latent geometries across Euclidean, spherical, and hyperbolic spaces.