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arXiv · 2410.04196

Improving Generalization with Flat Hilbert Bayesian Inference

Tuan Truong·Quyen Tran·Quan Pham-Ngoc·Nhat Ho·Dinh Phung·Trung Le
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Abstract

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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Tuan Truong, Quyen Tran, Quan Pham-Ngoc, Nhat Ho, Dinh Phung, Trung Le. 2024-10-05. Improving Generalization with Flat Hilbert Bayesian Inference. https://arxiv.org/abs/2410.04196

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