Dimension Reduction for Gaussian Process Models via Convex Combination of Kernels

Event Sponsor: 
Mathmatics and Computer Science Division Seminar - LANS
Start Date: 
Dec 5 2018 - 10:30am
Building/Room: 
Building 240/Room 4301
Location: 
Argonne National Laboratory
Speaker(s): 
Lulu Kang
Speaker(s) Title: 
Illinois Institute of Technology

Some engineering and scientific computer models that have high dimensional input space are actually only affected by a few essential input variables. If these active variables are identified, it would reduce the computation in the estimation of the Gaussian process (GP) model and help researchers understand the system modeled by the computer simulation. More importantly, reducing the input dimensions would also increase the prediction accuracy, as it alleviates the "curse of dimensionality" problem.

In this talk, we propose a new approach to reduce the input dimension of the Gaussian process model. Specifically, we develop an optimization method to identify a convex combination of a subset of kernels of lower dimensions from a large candidate set of kernels, as the correlation function for the GP model. To make sure a sparse subset is selected, we add a penalty on the weights of kernels. Several numerical examples are shown to show the advantages of the method. The proposed method has many connections with the existing methods including active subspace, additive GP, and composite GP models in the Uncertainty Quantification literature.
 

Miscellaneous Information: 

This seminar will be streamed. See details at https://anlpress.cels.anl.gov/cels-seminars/

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Upcoming Seminars
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November 13, 2018, "Quantifying the uncertainty in cardiovascular digital twins through model reduction, Bayesian inference and propagation using model ensembles." Daniele Schiavazzi, Assistant Professor, Department of Applied and Computational Mathematics and Statistics, Notre Dame
November 14, 2018, "Vishwas Rao MCS seminar, see www.anl.gov/event/computational-inference-and-forecasting-with-imperfect-data-and-models"
November 28, 2018, "Optimization for Machine Learning" Sven Leyffer, Senior Computational Mathematician, MCS/ANL
December 5, 2018, "Dimension Reduction for Gaussian Process Models via Convex Combination of Kernels" Lulu Kang, Associate Professor, Department of Applied Mathematics, Illinois Institute of Technology
December 12, 2018, "Advanced Modeling and Simulation of Solvent Extraction Systems - How Topological Data Analysis is Changing the Simulation Landscape" Michael Servis, Postdoctoral Researcher, Washington State University
January 9, 2019, "TBA" Hannah Morgan, Postdoctoral Appointee, MCS/ANL