改进贝叶斯推断中多峰分布的模式偏差问题
Correcting Mode Proportion Bias in Generalized Bayesian Inference via a Weighted Kernel Stein Discrepancy
- 引入加权核Stein差异，提升对多峰后验的敏感度
- 在多峰场景下显著改善模式识别能力，同时保持单峰稳健性
- 适合处理似然不可计算的复杂多峰模型
广义贝叶斯推断（GBI）通过使用非似然损失函数更新先验分布，增强了对模型误设的鲁棒性。然而，传统方法常面临似然不可计算的问题。近期研究利用核Stein差异（KSD）仅依赖对数似然梯度来解决此问题，但其仍存在对分离模式不敏感的严重缺陷。为此，本文提出一种加权核斯坦差异方法，在保持计算效率的同时有效捕捉多峰结构。该方法在处理似然不可计算的多峰后验时表现优异，且维持后验一致性与渐近正态性等关键理论性质。实验表明，相比标准KSD-Bayes，新方法在多峰场景下显著提升模式敏感度，同时在单峰设置及存在异常值时仍保持稳健性能。
原文摘要 · Abstract (English)
Generalized Bayesian Inference (GBI) provides a flexible framework for updating prior distributions using various loss functions instead of the traditional likelihoods, thereby enhancing the model robustness to model misspecification. However, GBI often suffers the problem associated with intractable likelihoods. Kernelized Stein Discrepancy (KSD), as utilized in a recent study, addresses this challenge by relying only on the gradient of the log-likelihood. Despite this innovation, KSD-Bayes suffers from critical pathologies, including insensitivity to well-separated modes in multimodal posteriors. To address this limitation, we propose a weighted KSD method that retains computational efficiency while effectively capturing multimodal structures. Our method improves the GBI framework for handling intractable multimodal posteriors while maintaining key theoretical properties such as posterior consistency and asymptotic normality. Experimental results demonstrate that our method substantially improves mode sensitivity compared to standard KSD-Bayes, while retaining robust performance in unimodal settings and in the presence of outliers.
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