## Description

Back to topGaussian 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

Back to top## Speakers

Back to top## Schedule

Back to top**Speaker: **Finn Lindgren (The University of Edinburgh)

**Speaker: **Connor Duffin (University of Cambridge)

**Speaker: **Francois Bachoc (Institut de Mathématiques de Toulouse)

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

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

**Speaker: **Emily Kang (University of Cincinnati)

**Speaker: **Yimin Xiao (Michigan State University)

**Speaker: **Arvind Saibaba (North Carolina State University)

**Speaker: **Matthias Katzfuss (Texas A&M University)

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

**Speaker: **Kristin Kirchner (Delft University of Technology)

**Speaker: **Douglas Nychka (Colorado School of Mines)

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

**Speaker: **Ruiyi Yang (Princeton University)

**Speaker: **Matt Plumlee (Northwestern University)

**Speaker: **Houman Owhadi (Caltech)

**Speaker: **Mamikon Gulian (Sandia National Laboratories)

**Speaker: **Aretha Teckentrup (University of Edinburgh)

**Speaker: **Maziar Raissi (University of Colorado Boulder)

## Poster Session

Back to topThe posters that have been submitted for the poster session are available on the poster session page.

## Videos

Back to topMaximum 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

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

Convergence rates of non-stationary and deep Gaussian process regression

Aretha Teckentrup

September 2, 2022