How Does Distribution Matching Help Domain Generalization: An Information-theoretic Analysis

TL;DR

This paper provides an information-theoretic analysis of distribution matching in domain generalization, revealing the complementary roles of gradient and representation alignment, and introduces IDM and PDM methods for improved robustness.

Contribution

It offers a novel probabilistic perspective on domain generalization, clarifies the roles of gradient and representation matching, and proposes new methods that outperform baselines.

Findings

Gradient and representation matching are complementary.

Existing methods focusing on one are insufficient.

IDM and PDM achieve superior performance.

Abstract

Domain generalization aims to learn invariance across multiple training domains, thereby enhancing generalization against out-of-distribution data. While gradient or representation matching algorithms have achieved remarkable success, these methods generally lack generalization guarantees or depend on strong assumptions, leaving a gap in understanding the underlying mechanism of distribution matching. In this work, we formulate domain generalization from a novel probabilistic perspective, ensuring robustness while avoiding overly conservative solutions. Through comprehensive information-theoretic analysis, we provide key insights into the roles of gradient and representation matching in promoting generalization. Our results reveal the complementary relationship between these two components, indicating that existing works focusing solely on either gradient or representation alignment are insufficient to solve the domain generalization problem. In light of these theoretical findings, we introduce IDM to simultaneously align the inter-domain gradients and representations. Integrated with the proposed PDM method for complex distribution matching, IDM achieves superior performance over various baseline methods.