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Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of…

The expressive power of Bayesian kernel-based methods has led them to become an important tool across many different facets of artificial intelligence, and useful to a plethora of modern application domains, providing both power and…

Overtaking in high-speed autonomous racing demands precise, real-time estimation of collision risk; particularly in wheel-to-wheel scenarios where safety margins are minimal. Existing methods for collision risk estimation either rely on…

Gaussian graphical regression is a powerful means that regresses the precision matrix of a Gaussian graphical model on covariates, permitting the numbers of the response variables and covariates to far exceed the sample size. Model fitting…

Based on the method by [K\"uc95], we give a procedure to list up all complete intersection Calabi--Yau manifolds with respect to direct sums of irreducible homogeneous vector bundles on Grassmannians for each dimension. In particular, we…

Multi-output Gaussian process (MGP) models have attracted significant attention for their flexibility and uncertainty-quantification capabilities, and have been widely adopted in multi-source transfer learning scenarios due to their ability…

Studies of Higgs boson properties are crucial for the understanding the Standard Model (SM), as it could couple to new particles and provide hints to physics Beyond the Standard Model (BSM). Different future colliders are proposed, among…

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…

Federated learning faces significant challenges in scenarios with heterogeneous data distributions and adverse network conditions, such as delays, packet loss, and data poisoning attacks. This paper proposes a novel method based on the…

This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…

We apply machine learning to the problem of finding numerical Calabi-Yau metrics. We extend previous work on learning approximate Ricci-flat metrics calculated using Donaldson's algorithm to the much more accurate "optimal" metrics of…

This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…

Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…

A dataset of fully quantum flux-flux correlation functions and reaction rate constants was constructed for organic heterogeneous catalytic surface reactions. Gaussian process regressors were successfully fitted to training data to predict…

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…

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…

We consider the problem of estimating the parameters of the covariance function of a Gaussian process by cross-validation. We suggest using new cross-validation criteria derived from the literature of scoring rules. We also provide an…

Gaussian process regression machine learning with a physically-informed kernel is used to model the phase compositions of nickel-base superalloys. The model delivers good predictions for laboratory and commercial superalloys, with $R^2>0.8$…

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To…