Hybrid Transfer Active Learning for Multistream Processes With Within-Process and Cross-Process Correlation Modeling and Online Updating

Active learning for regression (ALR) is a prevalent tool for learning functional relationships by selectively incorporating the most informative data. However, existing ALR methods suffer from the cold-start problem and focus solely on learning single-stream functions or processes. In this work, a hybrid transfer learning framework is proposed to model within-process and cross-process functional correlations for resolving the cold-start problem in multistream ALR. In this framework, a novel multioutput Gaussian process (MGP) covariance structure is proposed to characterize both within-process and cross-process correlations, and offline learning and online updating are strategically integrated to leverage these correlations for ALR. Specifically, offline learning utilizes cross-process correlation to transfer knowledge from related source processes, providing a robust prior for the target process, while online updating incorporates the offline-learned prior with newly collected data to iteratively update the within-process functional relationship in the target process. Theoretical justifications are provided for the proposed framework, showing that the ALR error decreases monotonically as new data are acquired under the guidance of the proposed learning structure. The accuracy and superiority of the proposed framework are thoroughly verified through comparisons with benchmark methods on various numerical and real-case studies.