Improving Generalization with Flat Hilbert Bayesian Inference

2024-10-05

arXiv.org

AI Summary

To address the limited generalization capability of conventional Bayesian inference, this paper proposes Flat Hilbert Bayesian Inference (FHBI): a novel framework that enforces flatness constraints on the posterior distribution within a reproducing kernel Hilbert space (RKHS) via alternating optimization between adversarial functional perturbations and functional gradient descent. FHBI is the first to extend generalization theory from finite-dimensional Euclidean spaces to infinite-dimensional function spaces, establishing both RKHS-based Bayesian posterior approximation and theoretically grounded generalization bounds. Evaluated on the VTAB-1K cross-domain benchmark comprising 19 datasets, FHBI consistently outperforms seven baseline methods, achieving substantial average performance gains—demonstrating its efficacy in enhancing generalization and robustness in function space. Key contributions include: (i) the theoretical extension of generalization analysis to infinite-dimensional function spaces; (ii) flatness-driven regularization of RKHS posteriors; and (iii) a new analytically tractable and scalable paradigm for Bayesian inference.

Technology Category

Machine Learning: Bayesian LearningReasoning under Uncertainty: Probabilistic InferenceSearch and Optimization: Learning to Search

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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 the reproducing kernel Hilbert spaces. 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 seven baseline methods on the 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.

Problem

• Enhance generalization in Bayesian inference
• Extend generalization analysis to infinite-dimensional spaces
• Outperform baselines on diverse datasets

Innovation

• FHBI enhances Bayesian inference generalization
• Uses adversarial and descent steps in RKHS
• Extends theory to infinite-dimensional spaces