Patchwork Kriging for Large Datasets

Event Sponsor: 
Mathmatics and Computer Science Division Seminar - LANS
Start Date: 
Jan 25 2019 - 10:30am
Building 240/Room 1404-1405
Argonne National Laboratory
Chiwoo Park
Speaker(s) Title: 
Florida State University

Gaussian process (GP) regression or stochastic kriging is a popular Bayesian nonparametric approach for nonlinear regression and simulation meta-modeling, but its omputation does not scale very well for large datasets. This talk presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, a technique for patching together the local GP models nearly seamlessly is introduced to ensure that the local GP models for two neighboring regions produce nearly the same response prediction and prediction error variance on the boundary between the two regions. This effectively solves the well-known discontinuity problem that degrades the boundary accuracy of existing local partitioned GP methods. Our main innovation is to represent the continuity conditions as additional pseudo-observations that the differences between neighboring GP responses are identically zero at an appropriately chosen set of boundary input locations. In contrast to heuristic continuity adjustments, this has an advantage of working within a formal GP framework, so that the GP-based predictive uncertainty quantification remains valid. This new approach also inherits a sparse block-like structure for the sample covariance matrix, which results in computationally efficient closed-form expressions for the predictive mean and variance. The numerical performance of the approach will be presented with comparison to several state-of-the-art approaches.

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Upcoming Seminars
January 9, 2019, "The impact of noise on Krylov method performance" Hannah Morgan, Postdoctoral Appointee, MCS/ANL
January 25, 2019, "Patchwork Kriging for Large Datasets" Chiwoo Park, Associate Professor, High Performance Material Institute, Florida State University
February 6, 2019, "Scalable Reinforcement-Learning-Based Neural Architecture Search for Scientific and Engineering Applications" Prasanna Balaprakash, Computer Scientist (MCS & LCF, ANL)
February 20, 2019, "SmartKT: A Search Framework to assist Program Comprehension using Smart Knowledge Transfer" Partha Pratim Das, Professor, Department of Computer Science & Engineering, Indian Institute of Technology Kharagpu