Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Nonlinear Regression, Estimation, and Inference

• Activity Number: 73 - Nonparametric Statistics in High-Dimensional Settings
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chih-Li Sung* and Wenjia Wang and Matthew Plumlee and Benjamin Haaland
• Companies: Georgia Institute of Technology and Georgia Institute of Technology and University of Michigan and Georgia Institute of Technology
• Keywords: computer experiment ; non-linear regression ; large-scale ; many-input ; overlapping group lasso

Abstract

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of GP models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as an accurate and computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. Consistency is shown and confidence intervals developed. Numeric examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy.