Covariance Function

Covariance functions are mathematical tools defining the relationships between data points in Gaussian process (GP) models, crucial for probabilistic predictions and uncertainty quantification. Current research emphasizes developing more flexible covariance functions to handle complex data structures, including non-stationary and sparsely correlated multi-output scenarios, often employing techniques like kernel convolutions and spike-and-slab priors within variational or expectation-maximization frameworks. These advancements improve the scalability and accuracy of GP models for diverse applications, such as time series analysis, system identification, and spatial modeling, while also enabling more efficient inference and interpretability through model reduction and the incorporation of prior knowledge.

Papers

September 5, 2024

Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior
Wang Xinming, Li Yongxiang, Yue Xiaowei, Wu Jianguo
Gaussian Process Non Stationary Multi Output Gaussian Process Stationary Kernel Covariance Function Spike and Slab

December 19, 2023

An Alternate View on Optimal Filtering in an RKHS
Benjamin Colburn, Jose C. Principe, Luis G. Sanchez Giraldo
Reproducing Kernel Hilbert Space Different Perspective Wiener Filter Adaptive RKHS Tikhonov Regularization Covariance Function Optimal Filter

October 4, 2023

Stationarity without mean reversion in improper Gaussian processes
Luca Ambrogioni
Gaussian Process Positive Definite Kernel Stationary Kernel Covariance Function GP Regression

August 27, 2023

Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes
Talay M Cheema, Carl Edward Rasmussen
Gaussian Process Many Sparse Fourier Feature Variational Approximation Sparse Variational Covariance Function Spatial Modelling

May 24, 2023

Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models
Siu Lun Chau, Krikamol Muandet, Dino Sejdinovic
Gaussian Process Shapley Value Stochastic Game Uncertain Reasoning Covariance Structure Covariance Function

April 25, 2023

Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation
Myeongjong Kang
Application Proficiency Evolutionary Algorithm Nonparametric Regression Positive Emotional Language Covariance Function Positive Definiteness Kernel Based Surrogate

September 24, 2022

One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels
Matthieu Darcy, Boumediene Hamzi, Giulia Livieri, Houman Owhadi, Peyman Tavallali
LeArning Abstract Stochastic Way Stochastic Differential Equation Function Approximation Interacting System Covariance Function Adaptive Kernel

August 26, 2022

Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations
Andreas Besginow, Markus Lange-Hegermann
Gaussian Process System Description Ordinary Differential Equation Covariance Function

June 17, 2022

March 14, 2022

On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernel
Chi-Ken Lu, Patrick Shafto
Latent Space Gaussian Process Neural Tangent Kernel Behavior Expressivity Style Covariance Conditioning Deep Gaussian Process Sinusoidal Activation Covariance Function

November 3, 2021

Scalable mixed-domain Gaussian process modeling and model reduction for longitudinal data
Juho Timonen, Harri Lähdesmäki
Gaussian Process Gaussian Process Regression Basis Function Covariance Function

Covariance Function

Papers

Non-stationary and Sparsely-correlated Multi-output Gaussian Process with Spike-and-Slab Prior

An Alternate View on Optimal Filtering in an RKHS

Stationarity without mean reversion in improper Gaussian processes

Integrated Variational Fourier Features for Fast Spatial Modelling with Gaussian Processes

Explaining the Uncertain: Stochastic Shapley Values for Gaussian Process Models

Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation

One-Shot Learning of Stochastic Differential Equations with Data Adapted Kernels

Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations

Shallow and Deep Nonparametric Convolutions for Gaussian Processes

On Integrating Prior Knowledge into Gaussian Processes for Prognostic Health Monitoring

On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernel

Scalable mixed-domain Gaussian process modeling and model reduction for longitudinal data