A Generalization Error Bound for Multi-class Domain Generalization

TL;DR

This paper provides a theoretical generalization error bound for multi-class domain generalization using a kernel-based algorithm, showing logarithmic scaling with the number of classes, and demonstrates empirical performance improvements.

Contribution

It introduces a novel generalization error bound for multi-class domain generalization and empirically validates the effectiveness of the proposed kernel-based algorithm.

Findings

Error bound scales logarithmically with number of classes

Proposed algorithm outperforms pooling strategies

Empirical results show significant performance gains

Abstract

Domain generalization is the problem of assigning labels to an unlabeled data set, given several similar data sets for which labels have been provided. Despite considerable interest in this problem over the last decade, there has been no theoretical analysis in the setting of multi-class classification. In this work, we study a kernel-based learning algorithm and establish a generalization error bound that scales logarithmically in the number of classes, matching state-of-the-art bounds for multi-class classification in the conventional learning setting. We also demonstrate empirically that the proposed algorithm achieves significant performance gains compared to a pooling strategy.