Gaussian Process Regression

Gaussian Process Regression (GPR) is a Bayesian non-parametric method used for regression tasks, aiming to predict a continuous output variable based on input data while providing uncertainty estimates. Current research emphasizes improving GPR's scalability and robustness, focusing on techniques like dividing local Gaussian processes for continual learning, tensor network methods for high-dimensional data, and efficient kernel selection and subsampling strategies. These advancements enhance GPR's applicability across diverse fields, including system identification, time series forecasting, safety-critical control systems, and scientific modeling where accurate uncertainty quantification is crucial.

Papers

October 4, 2022

Log-Linear-Time Gaussian Processes Using Binary Tree Kernels
Michael K. Cohen, Samuel Daulton, Michael A. Osborne
Gaussian Process Gaussian Process Regression Sparse Kernel Subtree Kernel Sparse GP

September 7, 2022

Non-Gaussian Process Regression
Yaman Kındap, Simon Godsill
Bayesian Inference Gaussian Process Regression Heavy Tailed Posterior Predictive Non Gaussianity

September 1, 2022

B\'ezier Gaussian Processes for Tall and Wide Data
Martin Jørgensen, Michael A. Osborne
Gaussian Process Gaussian Process Regression Predictive Performance Kernel Extension Approximate Inference

August 24, 2022

Fast emulation of density functional theory simulations using approximate Gaussian processes
Steven Stetzler, Michael Grosskopf, Earl Lawrence
Gaussian Process Gaussian Process Regression Particle Density Functional Theory

August 22, 2022

Scale invariant process regression: Towards Bayesian ML with minimal assumptions
Matthias Wieler
Visual Analogue Scale Regularization Model Gaussian Process Regression Modeling Assumption Kernel Regime Extrapolation Performance Kernel Optimization Invariant Smoothing

July 17, 2022

Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regression
Lixue Cheng, Jiace Sun, J. Emiliano Deustua, Vignesh C. Bhethanabotla, Thomas F. Miller
Known Molecule Gaussian Process Regression Electronic Structure C++ Implementation Potential Energy Surface Correlation Potential

July 16, 2022

A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression
Siavash Ameli, Shawn C. Shadden
Application Proficiency Gaussian Process Regression Covariance Matrix Source Identification Log Determinant

June 20, 2022

Noise Estimation in Gaussian Process Regression
Siavash Ameli, Shawn C. Shadden
Hyperparameter Optimization Gaussian Process Regression Noise Estimation Marginal Likelihood Hyperparameter Space Covariance Approximation

June 17, 2022

June 3, 2022

Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics
Jean-Luc Akian, Luc Bonnet, Houman Owhadi, Éric Savin
LeArning Abstract Raw Data Gaussian Process Regression Kernel Method Surrogate Modeling Reproducing Kernel Hilbert Space Aerodynamic Force Small Kernel Kernel Flow

May 25, 2022

Gradient-based explanations for Gaussian Process regression and classification models
Sarem Seitz
Gaussian Process Line by Line Explanation Gradient Based Gaussian Process Regression Classification Model Explainable Machine Learning Probabilistic Machine Learning

May 16, 2022

On the inability of Gaussian process regression to optimally learn compositional functions
Matteo Giordano, Kolyan Ray, Johannes Schmidt-Hieber
Gaussian Process Information Theoretic Gaussian Process Regression Function Composition

May 13, 2022

A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification
Cheng Chang, Tieyong Zeng
Uncertainty Quantification Gaussian Process Regression Boltzmann Distribution Deep Kernel Hybrid Physic Machine Learning

April 28, 2022

High Dimensional Bayesian Optimization with Kernel Principal Component Analysis
Kirill Antonov, Elena Raponi, Hao Wang, Carola Doerr
Bayesian Optimization Gaussian Process Regression Kernel Principal Component Analysis High Dimensional Bayesian Optimization Surrogate Based

April 20, 2022

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science
Kyle R. Lennon, Gareth H. McKinley, James W. Swan
Financial Application Data Driven Gaussian Process Regression Self Similar Experimental Data Soft Object Self Similarity

April 6, 2022

PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations
Jiahao Zhang, Shiqi Zhang, Guang Lin
Active Learning Loss Function Gaussian Process Inverse Problem Partial Differential Equation Gaussian Process Regression Physic Informed Gaussian Process

March 18, 2022

GiNGR: Generalized Iterative Non-Rigid Point Cloud and Surface Registration Using Gaussian Process Regression
Dennis Madsen, Jonathan Aellen, Andreas Morel-Forster, Thomas Vetter, Marcel Lüthi
Gaussian Process Regression Morphable Model Non Rigid Registration Surface Registration Non Rigid Point Cloud Coarse to finE Registration Deformation Prior Probabilistic Registration

March 17, 2022

Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed
Toni Karvonen, Chris J. Oates
Gaussian Process Gaussian Process Regression Maximum Likelihood

March 8, 2022

Evaluating feasibility of batteries for second-life applications using machine learning
Aki Takahashi, Anirudh Allam, Simona Onori
Machine Learning Gaussian Process Regression Task Feasibility Lithium Ion Battery Electric Vehicle Battery

Gaussian Process Regression

Papers

Log-Linear-Time Gaussian Processes Using Binary Tree Kernels

Non-Gaussian Process Regression

B\'ezier Gaussian Processes for Tall and Wide Data

Fast emulation of density functional theory simulations using approximate Gaussian processes

Scale invariant process regression: Towards Bayesian ML with minimal assumptions

Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regression

A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression

Noise Estimation in Gaussian Process Regression

Photoelectric Factor Prediction Using Automated Learning and Uncertainty Quantification

On Integrating Prior Knowledge into Gaussian Processes for Prognostic Health Monitoring

Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics

Gradient-based explanations for Gaussian Process regression and classification models

On the inability of Gaussian process regression to optimally learn compositional functions

A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification

High Dimensional Bayesian Optimization with Kernel Principal Component Analysis

A Data-Driven Method for Automated Data Superposition with Applications in Soft Matter Science

PAGP: A physics-assisted Gaussian process framework with active learning for forward and inverse problems of partial differential equations

GiNGR: Generalized Iterative Non-Rigid Point Cloud and Surface Registration Using Gaussian Process Regression

Maximum Likelihood Estimation in Gaussian Process Regression is Ill-Posed

Evaluating feasibility of batteries for second-life applications using machine learning