提出新型贝叶斯推断方法，兼顾鲁棒性与可计算性。
Robust Bayesian Inference via Variational Approximations of Generalized Rho-Posteriors
- 用软最大值替代原方法中的上确界，构建新后验分布
- 理论证明其在有限样本下具有明确收敛速率
- 适合需要稳定推断的复杂或含噪数据场景
我们引入了$ ilde{\rho}$-后验，即通过将竞争参数的上确界替换为软最大值聚合，得到的$\rho$-后验的改进版本。这一修改使得可对$ ilde{\rho}$-后验进行PAC-Bayesian分析，从而获得在有限样本下的泛化误差上界，并具备原始框架的关键鲁棒性：在模型误设和数据污染下仍能平滑退化。关键的是，这些PAC-Bayesian上界可推广至$ ilde{\rho}$-后验的变分近似，为高效推断提供理论保障。在指数族、回归及真实数据集上的数值实验表明，所提出的变分算法在计算成本与标准变分贝叶斯相当的前提下，实现了与理论预测相媲美的鲁棒性能。
原文摘要 · Abstract (English)
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.
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