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

arXiv: https://arxiv.org/abs/2605.18927 · HTML: https://mlsanity.com/paper/2605.18927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 18 May 2026.

## Builds on (most cited first, 12 of 12)

- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It](https://mlsanity.com/paper/1412.3730/) (2014)
- [Network structure from rich but noisy data](https://mlsanity.com/paper/1703.07376/) (2017)
- [The Geometry of Continuous Latent Space Models for Network Data](https://mlsanity.com/paper/1712.08641/) (2017)
- [Reconstructing networks with unknown and heterogeneous errors](https://mlsanity.com/paper/1806.07956/) (2018)
- [Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data](https://mlsanity.com/paper/1903.08977/) (2019)
- [Identifying the latent space geometry of network models through analysis of curvature](https://mlsanity.com/paper/2012.10559/) (2020)
- [Emergence of Soft Communities from Geometric Preferential Attachment](https://mlsanity.com/paper/1501.06835/) (2015)
- [Embedding Graphs in Lorentzian Spacetime](https://mlsanity.com/paper/1602.03103/) (2016)
- [Link prediction with hyperbolic geometry](https://mlsanity.com/paper/1903.08810/) (2019)
- [Latent Space Network Modelling with Hyperbolic and Spherical Geometries](https://mlsanity.com/paper/2109.03343/) (2021)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)

## Abstract (arXiv)

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.