Robust Bayesian Inference via Variational Approximations of Generalized Rho-Posteriors
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917362736824320 |
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| author | Khribch, EL Mahdi Alquier, Pierre |
| author_facet | Khribch, EL Mahdi Alquier, Pierre |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07325 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Bayesian Inference via Variational Approximations of Generalized Rho-Posteriors Khribch, EL Mahdi Alquier, Pierre Machine Learning Statistics Theory 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. |
| title | Robust Bayesian Inference via Variational Approximations of Generalized Rho-Posteriors |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2601.07325 |