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Dr Pulong Ma

Assistant Professor

Department of Statistics, 

Iowa State University


Residual Treed Gaussian Processes


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 treed GP (ResTGP). ResTGP combines key features of the treed GP (Gramacy and Lee 2008) and the multi-resolution GP (Fox and Dunson 2012), 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. This is joint work with Li Ma at Duke University.  

Speaker Biography

Pulong Ma is an assistant professor in Department of Statistics at Iowa State University. Prior to joining Iowa State, He was an assistant professor at Clemson University during 2021-2023 and was a postdoctoral fellow at the Statistical and Applied Mathematical Sciences Institute (SAMSI) and Duke University during 2018-2021. He got his PhD from University of Cincinnati in 2018. His research interests encompass Uncertainty Quantification, Spatial Statistics, Bayesian Statistics, and interdisciplinary research in remote sensing science, climate science, engineering, and medical science. His current work is focused on developing Bayesian tree-based methods and theory for Gaussian processes and statistical theory and methods for constructing new classes of multivariate and space-time covariance functions with long-range dependence. 

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