Transformation and Additivity in Gaussian Processes

We 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.