Can Domain Generalization be Guaranteed in Small-Sample Learning?

Title:Can Domain Generalization be Guaranteed in Small-Sample Learning?

Abstract:The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation and generalization. Structural Risk Minimization (SRM) has long been regarded as a principled solution under the classical i.i.d. assumption. However, domain generalization (DG) violates this assumption, leaving the theoretical role of SRM in DG largely unexplored. To bridge this gap, we establish the first theoretical guarantees for SRM in DG under mild assumptions. Specifically, based on the concept of stability, we derive learning consistency and generalization error bounds and prove that these bounds become tight when the hypotheses satisfy the stability condition. Building upon this, under a specific hypothesis space assumption, we establish stability, learning, and generalization bounds for SRM. We further discuss the applicability of these bounds to deep learning. This work establishes theoretical foundations for SRM under distribution shifts and sheds light on the design of robust DG algorithms in small-sample scenarios.

Machine Learning (cs.LG)

arXiv:2609.39512 [cs.LG]

(or arXiv:2609.39512v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.39512 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.