# Robust Bayesian Inference via Variational Approximations of Generalized Rho-Posteriors

arXiv: https://arxiv.org/abs/2601.07325 · HTML: https://mlsanity.com/paper/2601.07325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 12 Jan 2026.

## Abstract (arXiv)

We introduce the widetildeρ-posterior, a modified version of the ρ-posterior, obtained by replacing the supremum over competitor parameters with a softmax aggregation. This modification allows a PAC-Bayesian analysis of the widetildeρ-posterior. This yields finite-sample oracle inequalities with explicit convergence rates that inherit the key robustness properties of the original framework, in particular, graceful degradation under model misspecification and data contamination. Crucially, the PAC-Bayesian oracle inequalities extend to variational approximations of the widetildeρ-posterior, providing theoretical guarantees for tractable inference. Numerical experiments on exponential families, regression, and real-world datasets confirm that the resulting variational procedures achieve robustness competitive with theoretical predictions at computational cost comparable to standard variational Bayes.