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

近年来，一种涉及定量和序列因素的新型实验在科学和工程应用中引起了广泛的关注。在化疗中，为了开发包括多种药物成分的有效药物组合，研究人员需要进行实验，优化药物成分的剂量和顺序。由于输入空间是半离散的，并且随着药物数量的增加呈指数增长，这个问题给统计学家提出了新的挑战。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来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），需要插值和不确定性量化，这是目前文献中尚未解决的问题。在这个项目中，研究者将为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在涉及QS因素的应用中节省实验成本。应用于化疗将有助于推进美国的癌症研究，而应用于制造过程将提高美国的工业竞争力。该项目还为研究生提供了研究培训机会。实验中的主动学习，即广义机器学习背景下的强化学习，以自适应的方式分配运行，通常比单次实验更有效地优化实验设置。该项目将建立新的基于高斯过程的模型，用于具有QS因子的物理实验，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）输出的准确代理，这将促进不确定性量化和主动学习。最优的QS实验设计也将通过组合几个williams -transform好的点阵点集来构建，这些点阵点集具有空间填充、正交性和配对平衡等理想的性质。本研究项目将为科研和工业应用中感兴趣的各类QS实验提供系统的解决方案。该奖项反映了美国国家科学基金会的法定使命，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.