Multiresolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

• 成果类型: Article
• 署名作者: Sung, Chih-Li; Wang, Wenjia; Plumlee, Matthew; Haaland, Benjamin
• 署名单位: Michigan State University; Northwestern University; Utah System of Higher Education; University of Utah; University System of Georgia; Georgia Institute of Technology
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1595630
• 发表日期: 2020
• 页码: 908-919
• 关键词: prediction; selection; MODEL; interpolation; calibration; emulators; variance; Lasso

摘要

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multiresolution functional ANOVA (MRFA) model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input nonlinear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed MRFA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, in terms of both sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy. for this article are available online.