AMS2005-17: Gaussian processes and limiting linear models

Robert B. Gramacy, Herbert K. H. Lee
12/31/2005 09:00 AM
Applied Mathematics & Statistics
Gaussian processes (GPs) retain the linear model (LM) either as a special case, or in the limit. We show how this relationship can be exploited when the data are at least partially linear. However from the prospective of the Bayesian posterior, the GPs which encode the LM either have probability of nearly zero or are otherwise unattainable without the explicit construction of a prior with the limiting linear model (LLM) in mind. We develop such a prior, and show that its practical benefits extend well beyond the computational and conceptual simplicity of the LM. For example, linearity can be extracted on a per-dimension basis, or can be combined with treed partition models to yield a highly efficient nonstationary model. Our approach is demonstrated on synthetic and real datasets of varying linearity and dimensionality. Comparisons are made to other approaches in the literature.