Abstract

Gaussian processes (GP) enjoy wide popularity in spatial statistics, uncertainty quantification, and machine learning. With the advance of measurement technologies and increasing computing power, large numbers of measurements and large-scale numerical simulations make traditional GP models and computational strategies inadequate in dealing with spatially heterogeneous and big data, especially in multi-dimensional domains. In recent years, several multi-scale or tree-based extensions of the GP have been introduced to model spatial nonstationarity and/or achieve scalable computation. In this talk, I introduce a new Bayesian tree-based GP inference framework called residual tree GP (ResGP). ResTGP combines key features of the treed GP and the multi-resolution GP, thereby enjoying the computational efficiency of the formal and the flexibility of the latter. Our main idea is to decompose a Gaussian process as well as the data at a cascade of resolutions across locations through iteratively computing predictive and residual processes, thereby characterizing the underlying covariance structure and achieving divide-and-conquer on the data points simultaneously. We also introduce a new computational strategy for Bayesian inference for ResTGP that does not rely on Metropolis-Hastings based stochastic tree search algorithms but is based on recursive message passing.