Active learning provides guidance for the design and modeling of systems with highly expensive sampling costs. However, existing active learning approaches suffer from cold-start concerns, where the performance is impaired due to the initial few experiments designed by active learning. In this paper, we propose using transfer learning to solve the cold-start problem of functional regression by leveraging knowledge from related and data-rich signals to achieve robust and superior performance, especially when only a few experiments are available in the signal of interest. More specifically, we construct a multi-output Gaussian process (MGP) to model the between-signal functional relationship. This MGP features unique innovations that distinguish the proposed transfer active learning from existing works: i) a specially designed covariance structure is proposed for characterizing within-and between-signal inter-relationships and facilitating interpretable transfer learning, and ii) an iterative Bayesian framework is proposed to update the parameters and prediction of the MGP in real-time, which significantly reduces the computational load and facilitates the iterative active learning. The inter-relationship captured by this novel MGP is then fed into active learning using the integrated mean-squared error (IMSE) as the objective. We provide theoretical justifications for this active learning mechanism, which demonstrates the objective (IMSE) is monotonically decreasing as we gather more data from the proposed transfer active learning. The real-time updating and the monotonically decreasing objective together provide both practical efficiency and theoretical guarantees for solving the cold-start concern in active learning. The proposed method is compared with benchmark methods through various numerical and real case studies, and the results demonstrate the superiority of the method, especially when limited experiments are available at the initial stage of design.

中文翻译：

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基于多输出高斯过程的函数回归与预测实时迁移主动学习


主动学习为采样成本高昂的系统设计和建模提供指导。然而，现有的主动学习方法存在冷启动问题，由于主动学习设计的最初几个实验，性能会受到影响。在本文中，我们提议使用迁移学习来解决功能回归的冷启动问题，通过利用来自相关和数据丰富的信号的知识来实现稳健和卓越的性能，特别是当感兴趣的信号中只有少数实验可用时。更具体地说，我们构建了一个多输出高斯过程 （MGP） 来模拟信号之间的功能关系。该 MGP 具有独特的创新，将所提出的迁移主动学习与现有工作区分开来：i） 提出了一种专门设计的协方差结构，用于表征信号内和信号之间的相互关系，并促进可解释的迁移学习，以及 ii） 提出了一个迭代贝叶斯框架来实时更新 MGP 的参数和预测，这显着降低了计算负载并促进了迭代主动学习。 然后，以集成均方误差 （IMSE） 为目标，将这种新型 MGP 捕获的相互关系馈送到主动学习中。我们为这种主动学习机制提供了理论理由，它表明随着我们从提议的迁移主动学习中收集更多数据，目标 （IMSE） 正在单调递减。实时更新和单调递减目标共同为解决主动学习中的冷启动问题提供了实践效率和理论保障。 通过各种数值和实际案例研究，将所提出的方法与基准方法进行了比较，结果表明了该方法的优越性，尤其是在设计初始阶段实验有限的情况下。