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In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Variational inference techniques based on inducing variables provide an elegant framework for scalable posterior estimation in Gaussian process (GP) models. Besides enabling scalability, one of their main advantages over sparse…

Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…

This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…

Gravity inversion is a commonly applied data analysis technique in the field of geophysics. While machine learning methods have previously been explored for the problem of gravity inversion, these are deterministic approaches returning a…

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function,…

We formulate a reduced-order strategy for efficiently forecasting complex high-dimensional dynamical systems entirely based on data streams. The first step of our method involves reconstructing the dynamics in a reduced-order subspace of…

Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…

Gaussian process regression is a popular Bayesian framework for surrogate modeling of expensive data sources. As part of a broader effort in scientific machine learning, many recent works have incorporated physical constraints or other a…

Penalized regression methods, such as $L_1$ regularization, are routinely used in high-dimensional applications, and there is a rich literature on optimality properties under sparsity assumptions. In the Bayesian paradigm, sparsity is…

A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Gaussian processes (GP) are Bayesian non-parametric models that are widely used for probabilistic regression. Unfortunately, it cannot scale well with large data nor perform real-time predictions due to its cubic time cost in the data size.…

Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including…

In many areas of science and engineering, computer simulations are widely used as proxies for physical experiments, which can be infeasible or unethical. Such simulations can often be computationally expensive, and an emulator can be…

Recently, Gaussian processes have been used to model the vector field of continuous dynamical systems, referred to as GPODEs, which are characterized by a probabilistic ODE equation. Bayesian inference for these models has been extensively…

In this paper we propose a novel Bayesian solution for nonlinear regression in complex fields. Previous solutions for kernels methods usually assume a complexification approach, where the real-valued kernel is replaced by a complex-valued…

In Bayesian regression models with categorical predictors, constraints are needed to ensure identifiability when using all $K$ levels of a factor. The sum-to-zero constraint is particularly useful as it allows coefficients to represent…

In this work, we employ the Bayesian inference framework to solve the problem of estimating the solution and particularly, its derivatives, which satisfy a known differential equation, from the given noisy and scarce observations of the…