Expressing and Exploiting Structure in Modeling, Theory, and Computation with Gaussian Processes

Description

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Gaussian processes are widely used for prior modeling in data-centric applications including regression, classification, interpolation of computer output, and Bayesian inverse problems. However, despite their wide-spread adoption, practical and efficient ways of specifying flexible Gaussian processes are still lacking, particularly in the nonstationary case. In addition, Gaussian process methodology suffers from pressing computational challenges concerning their scalability to large datasets and high dimensional settings. This workshop will bring together computational and applied mathematicians, statisticians and subject matter researchers to push forward the modeling and computation with Gaussian processes, their novel use in classical scientific computing tasks, and the emerging theoretical analysis of the associated methodology.

A related but distinct challenge facing Gaussian process methodology is its computational scalability to large datasets. This tractability challenge, which stems from the need to compute the Cholesky factorization of a dense covariance matrix, has been at the forefront of researcher’s minds for decades, resulting in methods such as circulant embedding, Vecchia approximations, and the use of sparse representations. In recent times, new classes of approximation have appeared – including Hutchinson estimators for dealing with the trace terms of the likelihood and hierarchical off-diagonal low rank approximation of the covariance matrix which exploit the smoothness of the covariance kernel between well separated regions — that have the potential to vastly extend the scalability of Gaussian processes. These and other recent computational developments have facilitated the use of Gaussian processes with larger datasets and have also prompted a renewed interest in employing Gaussian processes in several classical scientific computing tasks such as numerical solution of partial differential equations, dimension reduction, and experimental design. However, a full understanding of the error caused by such computational techniques is still missing, and their scalability to high-dimensional settings needs further investigation.

There is a clear need to bring together computational and applied mathematicians, statisticians and subject matter researchers to push the field beyond its present practices, and in particular to investigate (a) new models that go beyond what, even under stationarity, are very narrow classes of stationary covariance functions; (b) how to express and understand the structure in the modeled process and exploit it in the computation phase; (c) novel application of Gaussian processes in classical scientific computing tasks; and (d) rigorous error analysis of the associated methodology.

This workshop will include a poster session for graduate students and postdocs. The application for proposing a poster will be available on this page after you register.

This workshop will take place in a hybrid format.

Organizers

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M A
Mihai Anitescu Argonne National Laboratory
D S
Daniel Sanz-Alonso University of Chicago
M S
Michael Stein Rutgers University

Speakers

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F B
Francois Bachoc Institut de Mathématiques de Toulouse
D B
David Bolin King Abdullah Univ. of Science and Technology (KAUST)
C D
Connor Duffin University of Cambridge
R G
Robert Gramacy Virginia Tech
M G
Mengyang Gu University of California, Santa Barbara
M G
Mamikon Gulian Sandia National Laboratories
E K
Emily Kang University of Cincinnati
M K
Matthias Katzfuss Texas A&M University
K K
Kristin Kirchner Delft University of Technology
F L
Finn Lindgren University of Edinburgh
D N
Douglas Nychka Colorado School of Mines
H O
Houman Owhadi Caltech
M P
Matt Plumlee Northwestern University
M R
Maziar Raissi University of Colorado Boulder
A S
Arvind Saibaba North Carolina State University
S S R
Suhasini Subba Rao Texas A&M University
A T
Aretha Teckentrup University of Edinburgh
Y X
Yimin Xiao Michigan State University
R Y
Ruiyi Yang Princeton University

Schedule

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Monday, August 29, 2022
9:10-9:15 CDT
Opening Remarks
9:15-10:15 CDT
Hierarchical models and computing with stochastic PDEs

Speaker: Finn Lindgren (The University of Edinburgh)

10:15-10:45 CDT
Break
10:45-11:45 CDT
Statistical Finite Elements for Nonlinear PDEs

Speaker: Connor Duffin (University of Cambridge)

11:45-13:00 CDT
Lunch
13:00-14:00 CDT
Maximum likelihood estimation for Gaussian processes under inequality constraints

Speaker: Francois Bachoc (Institut de Mathématiques de Toulouse)

14:00-15:00 CDT
Generalized probabilistic principal component analysis of microscopic and macroscopic dynamics

Speaker: Mengyang Gu (University of California, Santa Barbara (UCSB))

Tuesday, August 30, 2022
9:15-10:15 CDT
Graphical models for nonstationary time series

Speaker: Suhasini Subba Rao (Texas A&M University)

10:15-10:45 CDT
Break
10:45-11:45 CDT
Statistical Emulators for High-Dimensional Complex Forward Models in Remote Sensing

Speaker: Emily Kang (University of Cincinnati)

11:45-13:00 CDT
Lunch
13:00-14:00 CDT
Multivariate Gaussian Random Fields: Statistical and Sample Path Properties

Speaker: Yimin Xiao (Michigan State University)

14:00-15:00 CDT
Efficient solvers for Bayesian inverse problems and Gaussian random fields

Speaker: Arvind Saibaba (North Carolina State University)

15:00-15:30 CDT
Break
15:30-16:30 CDT
Scalable Gaussian-Process Inference Using Vecchia Approximations

Speaker: Matthias Katzfuss (Texas A&M University)

Wednesday, August 31, 2022
9:15-10:15 CDT
Deep Gaussian Process Surrogates for Computer Experiments

Speaker: Robert Gramacy (Virginia Polytechnic Institute & State University (Virginia Tech))

10:15-10:45 CDT
Break
10:45-11:45 CDT
Regularity and efficient simulation of Gaussian processes defined through SPDEs

Speaker: Kristin Kirchner (Delft University of Technology)

11:45-13:00 CDT
Lunch
13:00-14:00 CDT
Fast methods for conditional simulation

Speaker: Douglas Nychka (Colorado School of Mines)

14:00-16:00 CDT
Poster Session + Social Hour
Thursday, September 1, 2022
9:15-10:15 CDT
Gaussian Whittle-Matérn fields on metric graphs

Speaker: David Bolin (King Abdullah Univ. of Science and Technology (KAUST))

10:15-10:45 CDT
Break
10:45-11:45 CDT
Graph-Based Approximation of Matérn Gaussian Fields

Speaker: Ruiyi Yang (Princeton University)

11:45-13:00 CDT
Lunch
13:00-14:00 CDT
Large Scale Kriging by Substituting Optimization for Inversion

Speaker: Matt Plumlee (Northwestern University)

14:00-15:00 CDT
Computational Graph Completion

Speaker: Houman Owhadi (Caltech)

15:00-15:30 CDT
Break
15:30-16:30 CDT
Gaussian Process Regression Constrained by Boundary Value Problems

Speaker: Mamikon Gulian (Sandia National Laboratories)

Friday, September 2, 2022
9:15-10:15 CDT
Convergence rates of non-stationary and deep Gaussian process regression

Speaker: Aretha Teckentrup (University of Edinburgh)

10:15-10:45 CDT
Break
10:45-11:45 CDT
Physics-Informed Learning Machines

Speaker: Maziar Raissi (University of Colorado Boulder)


Poster Session

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The posters that have been submitted for the poster session are available on the poster session page.

Videos

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Hierarchical models and computing with stochastic PDEs

Finn Lindgren
August 29, 2022

Statistical Finite Elements for Nonlinear PDEs

Connor Duffin
August 29, 2022

Maximum likelihood estimation for Gaussian processes under inequality constraints

Francois Bachoc
August 29, 2022

Generalized probabilistic principal component analysis of microscopic and macroscopic dynamics

Mengyang Gu
August 29, 2022

Graphical models for nonstationary time series

Suhasini Subba Rao
August 30, 2022

Statistical Emulators for High-Dimensional Complex Forward Models in Remote Sensing

Emily Kang
August 30, 2022

Multivariate Gaussian Random Fields: Statistical and Sample Path Properties

Yimin Xiao
August 30, 2022

Efficient solvers for Bayesian inverse problems and Gaussian random fields

Arvind Saibaba
August 30, 2022

Scalable Gaussian-Process Inference Using Vecchia Approximations

Matthias Katzfuss
August 30, 2022

Deep Gaussian Process Surrogates for Computer Experiments

Robert Gramacy
August 31, 2022

Fast methods for conditional simulation

Douglas Nychka
August 31, 2022

Gaussian Whittle-Matérn fields on metric graphs

David Bolin
September 1, 2022

Graph-Based Approximation of Matérn Gaussian Fields

Ruiyi Yang
September 1, 2022

Large Scale Kriging by Substituting Optimization for Inversion

Matt Plumlee
September 1, 2022

Computational Graph Completion

Houman Owhadi
September 1, 2022

Gaussian Process Regression Constrained by Boundary Value Problems

Mamikon Gulian
September 1, 2022

Convergence rates of non-stationary and deep Gaussian process regression

Aretha Teckentrup
September 2, 2022

Physics-Informed Learning Machines

Maziar Raissi
September 2, 2022