Transformation and Additivity in Gaussian Processes
Li‐Hsiang Lin, V. Roshan Joseph · Technometrics · 2019
Li-Hsiang Lina & V. Roshan Joseph*aa H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GAColor versions of one or more of the figures in the article can be found online at www.tandfonline.com/r/TECH.Contact V. Roshan Joseph [email protected] H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332.AbstractWe discuss the problem of approximating a deterministic function using Gaussian processes (GPs). The role of transformation in GP modeling is not well understood. We argue that transformation of the response can be used for making the deterministic function approximately additive, which can then be easily estimated using an additive GP. We call such a GP a transformed additive Gaussian (TAG) process. To capture possible interactions which are unaccounted for in an additive model, we propose an extension of the TAG process called transformed approximately additive Gaussian (TAAG) process. We develop efficient techniques for fitting a TAAG process. In fact, we show that it can be fitted to high-dimensional data much more efficiently than a standard GP. Furthermore, we show that the use of the TAAG process leads to better estimation, interpretation, visualization, and prediction. The proposed methods are implemented in the R package TAG.