小样本学习中能否保证域泛化？
Can Domain Generalization be Guaranteed in Small-Sample Learning?
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中文总结 AI 辅助
本研究首次为小样本学习中的域泛化问题下的结构风险最小化提供了理论保证，基于稳定性推导了紧致的学习与泛化误差界，并探讨了其在深度学习中的适用性。
中文摘要 AI 辅助
小样本学习问题仍然是机器学习中的一个基本挑战，因为有限的训练数据导致模型估计和泛化不稳定。结构风险最小化（SRM）长期以来被视为经典独立同分布（i.i.d.）假设下的原则性解决方案。然而，域泛化（DG）违反了这一假设，使得SRM在DG中的理论作用在很大程度上未被探索。为了弥合这一差距，我们在温和假设下为DG中的SRM建立了首个理论保证。具体而言，基于稳定性的概念，我们推导了学习一致性和泛化误差界，并证明当假设满足稳定性条件时，这些界变得紧致。在此基础上，在特定的假设空间假设下，我们为SRM建立了稳定性、学习和泛化界。我们进一步讨论了这些界在深度学习中的适用性。这项工作为分布偏移下的SRM奠定了理论基础，并为小样本场景中鲁棒DG算法的设计提供了启示。
英文摘要
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.
