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Gaussian Processes (GPs) are flexible, nonparametric Bayesian models widely used for regression and classification because of their ability to capture complex data patterns and quantify predictive uncertainty. However, the O(n^3)…

Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision,…

We present a new strategy for learning the functional relation between a pair of variables, while addressing inhomogeneities in the correlation structure of the available data, by modelling the sought function as a sample function of a…

Constructing a classical potential suited to simulate a given atomic system is a remarkably difficult task. This chapter presents a framework under which this problem can be tackled, based on the Bayesian construction of nonparametric force…

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…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Gaussian Processes (GPs) offer an attractive method for regression over small, structured and correlated datasets. However, their deployment is hindered by computational costs and limited guidelines on how to apply GPs beyond simple…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often…

In this paper we introduce a novel framework for making exact nonparametric Bayesian inference on latent functions, that is particularly suitable for Big Data tasks. Firstly, we introduce a class of stochastic processes we refer to as…

Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate…

Transformed Gaussian Processes (TGPs) are stochastic processes specified by transforming samples from the joint distribution from a prior process (typically a GP) using an invertible transformation; increasing the flexibility of the base…

Gaussian processes (GPs) are non-linear probabilistic models popular in many applications. However, na\"ive GP realizations require quadratic memory to store the covariance matrix and cubic computation to perform inference or evaluate the…

Research on Poisson regression analysis for dependent data has been developed rapidly in the last decade. One of difficult problems in a multivariate case is how to construct a cross-correlation structure and at the meantime make sure that…

This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…

The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…

Gaussian processes (GPs) are Bayesian non-parametric models popular in a variety of applications due to their accuracy and native uncertainty quantification (UQ). Tuning GP hyperparameters is critical to ensure the validity of prediction…

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…

A Gaussian process (GP) is a powerful and widely used regression technique. The main building block of a GP regression is the covariance kernel, which characterizes the relationship between pairs in the random field. The optimization to…