Towards a Theoretical Framework of Out-of-Distribution Generalization

2021/06/08 by Haotian Ye, Chuanlong Xie, Ye, Haotian +9 · 41 citations
Computer Science · Mathematics · #Anomaly Detection Techniques and Applications #Artificial intelligence #Benchmark (surveying) #Computer science #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Function (biology) #Generalization #Geography #Invariant (physics) #Machine Learning (cs.LG) #Machine Learning and Data Classification #Machine learning #Mathematics #Model selection #Variance (accounting) #cs.LG

paper · pdf · doi:10.48550/arxiv.2106.04496

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2021/06/08 · arxiv created 2021/11/08 · arxiv updated 2021/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Generalization to out-of-distribution (OOD) data is one of the central problems in modern machine learning. Recently, there is a surge of attempts to propose algorithms that mainly build upon the idea of extracting invariant features. Although intuitively reasonable, theoretical understanding of what kind of invariance can guarantee OOD generalization is still limited, and generalization to arbitrary out-of-distribution is clearly impossible. In this work, we take the first step towards rigorous and quantitative definitions of 1) what is OOD; and 2) what does it mean by saying an OOD problem is learnable. We also introduce a new concept of expansion function, which characterizes to what extent the variance is amplified in the test domains over the training domains, and therefore give a quantitative meaning of invariant features. Based on these, we prove OOD generalization error bounds. It turns out that OOD generalization largely depends on the expansion function. As recently pointed out by Gulrajani and Lopez-Paz (2020), any OOD learning algorithm without a model selection module is incomplete. Our theory naturally induces a model selection criterion. Extensive experiments on benchmark OOD datasets demonstrate that our model selection criterion has a significant advantage over baselines.

Citations

• A unifying view on dataset shift in classification
• Gradient-based learning applied to document recognition
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• Invariant Risk Minimization
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• In Search of Lost Domain Generalization
• Learning explanations that are hard to vary
• Enforcing Predictive Invariance across Structured Biomedical Domains
• Understanding the Failure Modes of Out-of-Distribution Generalization
• Empirical or Invariant Risk Minimization? A Sample Complexity Perspective
• WILDS: A Benchmark of in-the-Wild Distribution Shifts
• Does Invariant Risk Minimization Capture Invariance?
• Out-of-Distribution Generalization Analysis via Influence Function
• Risk Variance Penalization

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