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Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Sparse variational Gaussian process (SVGP) methods are a common choice for non-conjugate Gaussian process inference because of their computational benefits. In this paper, we improve their computational efficiency by using a dual…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

The Gaussian process (GP) is a powerful tool for nonparametric modeling, but its sensitivity to outliers limits its applicability to data distributions with heavy-tails. Studentt processes offer a robust alternative for heavy tail modeling,…

Gaussian Process (GP) models are popular tools in uncertainty quantification (UQ) because they purport to furnish functional uncertainty estimates that can be used to represent model uncertainty. It is often difficult to state with…

Bayesian model updating based on Gaussian Process (GP) models has received attention in recent years, which incorporates kernel-based GPs to provide enhanced fidelity response predictions. Although most kernel functions provide high fitting…

Physically motivated Gaussian process (GP) kernels for stellar variability, like the commonly used damped, driven simple harmonic oscillators that model stellar granulation and p-mode oscillations, quantify the instantaneous covariance…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

Accommodating long sequences efficiently in autoregressive Transformers, especially within an extended context window, poses significant challenges due to the quadratic computational complexity and substantial KV memory requirements…

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…

Kernel selection plays a central role in determining the performance of Gaussian Process (GP) models, as the chosen kernel determines both the inductive biases and prior support of functions under the GP prior. This work addresses the…

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

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…

Motivated by the needs of selecting important features for massive neuroimaging data, we propose a spatially varying coefficient model (SVCMs) with sparsity and piecewise smoothness imposed on the coefficient functions. A new class of…

Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix.…

Rotation equivariant graph neural networks, i.e. networks designed to guarantee certain geometric relations between their inputs and outputs, yield state of the art performance on spatial deep learning tasks. They exhibit high data…

We propose a method (TT-GP) for approximate inference in Gaussian Process (GP) models. We build on previous scalable GP research including stochastic variational inference based on inducing inputs, kernel interpolation, and structure…

Self-attention in transformer models is an incremental associative memory that maps key vectors to value vectors. One way to speed up self-attention is to employ GPU-compatible vector search algorithms based on standard partitioning methods…

Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…