Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors
For practitioners using Bayesian latent space models for network analysis, this work addresses a critical robustness issue caused by model misspecification, offering a principled fix that enhances reliability.
Bayesian latent space models for graphs are misspecified under real-world conditions, leading to overconfident and poorly calibrated inference. The proposed generalized posterior framework, Link-Sequential R-SafeBayes, improves calibration and link prediction, and reliably selects latent geometries across Euclidean, spherical, and hyperbolic spaces.
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.