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arXiv · 2402.07834

Generalizing across Temporal Domains with Koopman Operators

Qiuhao Zeng·Wei Wang·Fan Zhou·Gezheng Xu·Ruizhi Pu·Changjian Shui·Christian Gagne·Shichun Yang·Boyu Wang·Charles X. Ling
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Abstract

In the field of domain generalization, the task of constructing a predictive model capable of generalizing to a target domain without access to target data remains challenging. This problem becomes further complicated when considering evolving dynamics between domains. While various approaches have been proposed to address this issue, a comprehensive understanding of the underlying generalization theory is still lacking. In this study, we contribute novel theoretic results that aligning conditional distribution leads to the reduction of generalization bounds. Our analysis serves as a key motivation for solving the Temporal Domain Generalization (TDG) problem through the application of Koopman Neural Operators, resulting in Temporal Koopman Networks (TKNets). By employing Koopman Operators, we effectively address the time-evolving distributions encountered in TDG using the principles of Koopman theory, where measurement functions are sought to establish linear transition relations between evolving domains. Through empirical evaluations conducted on synthetic and real-world datasets, we validate the effectiveness of our proposed approach.

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Qiuhao Zeng, Wei Wang, Fan Zhou, Gezheng Xu, Ruizhi Pu, Changjian Shui, Christian Gagne, Shichun Yang, Boyu Wang, Charles X. Ling. 2024-02-15. Generalizing across Temporal Domains with Koopman Operators. https://arxiv.org/abs/2402.07834

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