A0416
Title: Residual tree Gaussian processes
Authors: Pulong Ma - Iowa State University (United States) [presenting]
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. A new Bayesian tree-based GP inference framework, called residual treed GP (ResTGP), is introduced. ResTGP integrates the divide-and-conquer and the multi-scale modeling strategies, thereby enjoying the computational efficiency of the formal and the flexibility of the latter. The 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. A new computational strategy is also introduced for Bayesian inference for ResTGP that does not rely on Metropolis-Hastings-based stochastic tree search algorithms but is based on recursive message passing.
