Related papers: From Local Interactions to Global Operators: Scala…

Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…

We provide a new approach to approximate emulation of large computer experiments. By focusing expressly on desirable properties of the predictive equations, we derive a family of local sequential design schemes that dynamically define the…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention. We develop SigGPDE, a new scalable sparse variational inference framework…

Gaussian Process (GP) Variational Autoencoders (VAEs) extend standard VAEs by replacing the fully factorised Gaussian prior with a GP prior, thereby capturing richer correlations among latent variables. However, performing exact GP…

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data,…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Deformable retinal image registration is notoriously difficult due to large homogeneous regions and sparse but critical vascular features, which cause limited gradient signals in standard learning-based frameworks. In this paper, we…

We develop a novel framework to accelerate Gaussian process regression (GPR). In particular, we consider localization kernels at each data point to down-weigh the contributions from other data points that are far away, and we derive the GPR…

Learning expressive kernels while retaining tractable inference remains a central challenge in scaling Gaussian processes (GPs) to large and complex datasets. We propose a scalable GP regressor based on deep basis kernels (DBKs). Our DBK is…

Gaussian process (GP) emulators have become essential tools for approximating complex simulators, significantly reducing computational demands in optimization, sensitivity analysis, and model calibration. While traditional GP emulators…

We study the deterministic global optimization of trained Gaussian process posterior mean functions over hyperrectangular domains. Although the posterior mean function has a compact closed-form representation, its global optimization is…

Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…

Accurate human motion prediction with well-calibrated uncertainty is critical for safe human-robot collaboration (HRC), where robots must anticipate and react to human movements in real time. We propose a structured multitask variational…

Numerically solving partial differential equations (PDEs) can be challenging and computationally expensive. This has led to the development of reduced-order models (ROMs) that are accurate but faster than full order models (FOMs). Recently,…

Gaussian processes are powerful models for probabilistic machine learning, but are limited in application by their $O(N^3)$ inference complexity. We propose a method for deriving parametric families of kernel functions with compact spatial…

Gaussian processes (GPs) are an important tool in machine learning and statistics with applications ranging from social and natural science through engineering. They constitute a powerful kernelized non-parametric method with…

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…