Abstract:

Factor screening and optimization of both quantitative and qualitative (QQ) factors are critical in several recent applications where evaluating black-box systems is resource-intensive or time-consuming. Moreover, some qualitative factors in QQ may involve many levels. Yet, most current screening methods focus on factors, but cannot identify important qualitative levels. To address these challenges, we propose a novel penalized additive Gaussian process (PAGP), featuring an interpretable additive covariance structure for QQ factors. It allows for sparsity penalties on the hyper-parameters of the covariance structure, which enables the identification of important qualitative levels. A tailored alternating direction method of multipliers is developed to optimize the L1 regularized likelihood, and a gradient-informed optimization approach using derivative information is proposed to accelerate PAGP modeling. We further establish an effective approach leveraging Shapley values for screening quantitative factors. Then, a Bayesian optimization (BO) approach leveraging the desirable uncertainty quantification of PAGP is proposed to optimize black-box systems with QQ factors. This PAGP-based Bayesian optimization can provide an interpretable importance attribution of factor levels during optimization. Simulations and real case studies illustrate the superior performance of the proposed methods compared to some state-of-the-art approaches.

Bio: 

肖骞，上海交通大学统计系长聘副教授。他于2017年在美国UCLA获得统计学博士学位，后加入美国佐治亚大学统计系历任助理教授、长聘副教授，于2024年加入上海交通大学。他的主要研究方向包括计算机试验设计与分析、不确定性量化等。他的研究成果发表在AOS，JASA，Biometrika、Technometrics等顶尖统计学期刊上。他获国家级青年人才计划资助，主持国家重点研发青年科学家项目、小米青年学者项目等。