Related papers: SEEK: Self-adaptive Explainable Kernel For Nonstat…

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve…

Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse…

Choosing the most adequate kernel is crucial in many Machine Learning applications. Gaussian Process is a state-of-the-art technique for regression and classification that heavily relies on a kernel function. However, in the Gaussian…

Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…

Robotic Information Gathering (RIG) relies on the uncertainty of a probabilistic model to identify critical areas for efficient data collection. Gaussian processes (GPs) with stationary kernels have been widely adopted for spatial modeling.…

Gaussian processes (GPs) are used to make medical and scientific decisions, including in cardiac care and monitoring of atmospheric carbon dioxide levels. Notably, the choice of GP kernel is often somewhat arbitrary. In particular,…

Uncertainty quantification (UQ) over graphs arises in a number of safety-critical applications in network science. The Gaussian process (GP), as a classical Bayesian framework for UQ, has been developed to handle graph-structured data by…

Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…

Natural language processing often involves computations with semantic or syntactic graphs to facilitate sophisticated reasoning based on structural relationships. While convolution kernels provide a powerful tool for comparing graph…

This paper discusses a special kind of a simple yet possibly powerful algorithm, called single-kernel Gradraker (SKG), which is an adaptive learning method predicting unknown nodal values in a network using known nodal values and the…

Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…

The Gaussian process state-space model (GPSSM) has garnered considerable attention over the past decade. However, the standard GP with a preliminary kernel, such as the squared exponential kernel or Mat\'{e}rn kernel, that is commonly used…

Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input…

Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…

We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…

Gaussian processes (GPs) can provide a principled approach to uncertainty quantification with easy-to-interpret kernel hyperparameters, such as the lengthscale, which controls the correlation distance of function values. However, selecting…

In this paper we propose a family of tractable kernels that is dense in the family of bounded positive semi-definite functions (i.e. can approximate any bounded kernel with arbitrary precision). We start by discussing the case of stationary…

We develop a flexible Gaussian Process (GP) framework for learning the covariance structure of Age- and Year-specific mortality surfaces. Utilizing the additive and multiplicative structure of GP kernels, we design a genetic programming…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…

Belonging to the family of Bayesian nonparametrics, Gaussian process (GP) based approaches have well-documented merits not only in learning over a rich class of nonlinear functions, but also in quantifying the associated uncertainty.…