Covariance Kernel

Covariance kernels are fundamental components of Gaussian processes (GPs), defining the relationships between data points and shaping the resulting predictive distributions. Current research focuses on developing more expressive and computationally efficient kernels, including those derived from deep neural networks and those designed for specific data structures like graphs and spatiotemporal data, often employing techniques like inducing points and sparse grids to improve scalability. These advancements are crucial for extending the applicability of GPs to larger datasets and more complex problems in diverse fields, such as machine learning, scientific modeling, and engineering applications where robust uncertainty quantification is essential.

Papers

October 25, 2024

On the Benefits of Active Data Collection in Operator Learning
Unique Subedi, Ambuj Tewari
Operator Learning Complementary Benefit Data Collection Covariance Kernel

October 2, 2024

Deep Kernel Posterior Learning under Infinite Variance Prior Weights
Jorge Loría, Anindya Bhadra
Shallow Neural Network Bayesian Deep Learning Deep Kernel Learning Unbounded Variance Covariance Kernel

August 29, 2024

Statistical and Geometrical properties of regularized Kernel Kullback-Leibler divergence
Clémentine Chazal, Anna Korba, Francis Bach
Kullback Leibler Divergence Geometric Feature Kernel Extension Covariance Kernel

June 13, 2024

Deep Sketched Output Kernel Regression for Structured Prediction
Tamim El Ahmad, Junjie Yang, Pierre Laforgue, Florence d'Alché-Buc
Structured Output Structured Prediction Covariance Kernel Kernel Induced Loss

May 22, 2024

Efficient Two-Stage Gaussian Process Regression Via Automatic Kernel Search and Subsampling
Shifan Zhao, Jiaying Lu, Ji Yang (Carl), Edmond Chow, Yuanzhe Xi
Uncertainty Quantification Gaussian Process Regression Covariance Kernel

December 22, 2023

Sample Path Regularity of Gaussian Processes from the Covariance Kernel
Nathaël Da Costa, Marvin Pförtner, Lancelot Da Costa, Philipp Hennig
Gaussian Process Sample Path Covariance Kernel

May 23, 2023

Kernel Interpolation with Sparse Grids
Mohit Yadav, Daniel Sheldon, Cameron Musco
Kernel Matrix Kernel Interpolation Covariance Kernel

February 19, 2023

Non-separable Covariance Kernels for Spatiotemporal Gaussian Processes based on a Hybrid Spectral Method and the Harmonic Oscillator
Dionissios T. Hristopulos
Gaussian Process Spectral Method Harmonic Oscillator Covariance Kernel

February 12, 2023

Graph Neural Network-Inspired Kernels for Gaussian Processes in Semi-Supervised Learning
Zehao Niu, Mihai Anitescu, Jie Chen
Semi Supervised Learning Gaussian Process Graph Structured Data Graph Neural Graph Kernel Small Kernel Covariance Kernel

November 4, 2022

Fully Bayesian inference for latent variable Gaussian process models
Suraj Yerramilli, Akshay Iyer, Wei Chen, Daniel W. Apley
Gaussian Process Bayesian Inference Covariance Kernel

July 30, 2022

Doubly Deformable Aggregation of Covariance Matrices for Few-shot Segmentation
Zhitong Xiong, Haopeng Li, Xiao Xiang Zhu
Semantic Segmentation Model Shot Segmentation Covariance Matrix Feature Aggregation Covariance Kernel

April 21, 2022

Inducing Gaussian Process Networks
Alessandro Tibo, Thomas Dyhre Nielsen
Gaussian Process Kernel Approximation Covariance Kernel