Bridging Domains with Approximately Shared Features

Multi-source domain adaptation aims to reduce performance degradation when applying machine learning models to unseen domains. A fundamental challenge is devising the optimal strategy for feature selection. Existing literature is somewhat paradoxical: some advocate for learning invariant features from source domains, while others favor more diverse features. To address the challenge, we propose a statistical framework that distinguishes the utilities of features based on the variance of their correlation to label $y$ across domains. Under our framework, we design and analyze a learning procedure consisting of learning approximately shared feature representation from source tasks and fine-tuning it on the target task. Our theoretical analysis necessitates the importance of learning approximately shared features instead of only the strictly invariant features and yields an improved population risk compared to previous results on both source and target tasks, thus partly resolving the paradox mentioned above. Inspired by our theory, we proposed a more practical way to isolate the content (invariant+approximately shared) from environmental features and further consolidate our theoretical findings.