In many open environment applications, data are collected in the form of a stream, which exhibits an evolving distribution over time. How to design algorithms to track these evolving data distributions with provable guarantees, particularly in terms of the generalization ability, remains a formidable challenge. To handle this crucial but rarely studied problem and take a further step toward robust artificial intelligence, we propose a novel framework called Distribution Adaptable Learning (DAL). It enables the model to effectively track the evolving data distributions. By Encoding Feature Marginal Distribution Information (EFMDI), we broke the limitations of optimal transport to characterize the environmental changes and enable model reuse across diverse data distributions. It can enhance the reusable and evolvable properties of DAL in accommodating evolving distributions. Furthermore, to obtain the model interpretability, we not only analyze the generalization error bound of the local step in the evolution process, but also investigate the generalization error bound associated with the entire classifier trajectory of the evolution based on the Fisher-Rao distance. For demonstration, we also present two special cases within the framework, together with their optimizations and convergence analyses. Experimental results over both synthetic and real-world data distribution evolving tasks validate the effectiveness and practical utility of the proposed framework.
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