通过函数空间对抗扰动提升贝叶斯推断的泛化能力
Improving Generalization with Flat Hilbert Bayesian Inference
- 在再生核希尔伯特空间中迭代进行对抗扰动与函数下降
- 在VTAB-1K上9个基线方法均被超越，平均性能提升显著
- 适合关注模型泛化与理论严谨性的机器学习研究者
我们提出平坦希尔伯特贝叶斯推断（FHBI），一种旨在提升贝叶斯推断泛化能力的算法。该方法基于再生核希尔伯特空间中的迭代两步过程，包含对抗性函数扰动和函数下降步骤。理论分析将先前在有限维欧氏空间中的泛化能力结论拓展至无限维函数空间。为评估有效性，我们在涵盖19个不同领域、具有多样化语义的 exttt{VTAB-1K}基准上，与九种基线方法进行了全面对比。实验结果表明，FHBI始终以显著优势超越基线，充分验证了其实际有效性。
原文摘要 · Abstract (English)
We introduce Flat Hilbert Bayesian Inference (FHBI), an algorithm designed to enhance generalization in Bayesian inference. Our approach involves an iterative two-step procedure with an adversarial functional perturbation step and a functional descent step within a reproducing kernel Hilbert space. This methodology is supported by a theoretical analysis that extends previous findings on generalization ability from finite-dimensional Euclidean spaces to infinite-dimensional functional spaces. To evaluate the effectiveness of FHBI, we conduct comprehensive comparisons against nine baseline methods on the \texttt{VTAB-1K} benchmark, which encompasses 19 diverse datasets across various domains with diverse semantics. Empirical results demonstrate that FHBI consistently outperforms the baselines by notable margins, highlighting its practical efficacy.
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