Collaborative Research: Design, Modeling and Active Learning of Quantitative-Sequence Experiments

近年来，一种新型的定量因子和序列因子实验在科学和工程应用中引起了极大的关注。在化疗中，为了开发涉及多种药物成分的有效药物组合，研究人员需要进行优化药物成分剂量和顺序的实验。这一问题给统计学家提出了新的挑战，因为输入空间是半离散的，并且随着药物数量呈指数级增长。研究人员比以往任何时候都更依赖于统计建模和主动学习，以确定有限的实验资源的最佳设置。此外，QS实验通常有特定的要求。在金属增材制造过程的计算机实验中，输出响应是二元的（成功/失败），并且它需要插值和不确定性量化，这是当前文献中未解决的问题。在这个项目中，研究人员将为QS实验提供系统的解决方案，解决设计，建模，不确定性量化和主动学习方面的挑战。该项目的成果将有助于节省涉及QS因子的应用中的实验成本。在化疗中的应用将有助于推进美国的癌症研究，而在制造过程中的应用将提高美国的工业竞争力。此外，该项目还为研究生提供了研究培训的机会。实验中的主动学习，也就是在机器学习的广泛背景下的强化学习，以自适应的方式分配运行，这通常比一次性实验更有效地优化实验设置。本计画将建立以高斯过程为基础的QS因子物理实验新模式，并在此基础上开发新的主动学习程序。为了分析计算机实验，将建立一个新的Hopfield过程（HP）框架作为插值二进制（和分类）输出的准确替代，这将有助于不确定性量化和主动学习。最优QS实验设计也将通过组合几个Williams变换的好格点集来构造，这些格点集具有理想的性质，包括空间填充，正交性和配对平衡。该研究项目将为科学研究和工业应用中感兴趣的各种类型的QS实验提供系统的解决方案。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

A new type of experiment concerning both quantitative and sequence (QS) factors has recently drawn great attention in science and engineering applications. In chemotherapy, to develop efficient drug combinations involving several drug components, researchers need to conduct experiments optimizing both the doses and the sequence orders of drug components. Such a problem raises new challenges for statisticians since the input space is semi-discrete and grows exponentially with the number of drugs. Researchers rely more than ever on statistical modeling and active learning to identify optimal settings given limited experimental resources. Additionally, QS experiments often have specific requirements. In the computer experiment for metal additive manufacturing processes, the output response is binary (success/failure), and it requires both interpolation and uncertainty quantification, which is an unsolved problem in the current literature. In this project, the investigators will provide systematic solutions to QS experiments, addressing challenges in design, modeling, uncertainty quantification, and active learning. The outcome of this project will help save experimental costs in applications involving QS factors. The applications to chemotherapy will help advance cancer research in the U.S., while the applications to manufacturing processes will enhance the industrial competitiveness of the U.S. Also, this project provides research training opportunities for graduate students. Active learning in experiments, aka reinforcement learning under the broad context of machine learning, allocates runs in an adaptive manner, which is generally more efficient than one-shot experiments for optimizing the experimental settings. This project will establish new Gaussian process-based models for physical experiments with QS factors, based on which new active learning procedures will be developed. For analyzing computer experiments, a novel Hopfield process (HP) framework will be established as an accurate surrogate for interpolating binary (and categorical) outputs, which will facilitate uncertainty quantification and active learning. Optimal QS experimental designs will also be constructed by combing several Williams-transformed good lattice point sets, which possess desirable properties including space-filling, orthogonality, and paired balance. This research project will provide systematic solutions for various types of QS experiments that are of interest in scientific research and industrial applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.