Related papers: Additive Covariance Kernels for High-Dimensional G…

Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…

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…

In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…

We present a practical way of introducing convolutional structure into Gaussian processes, making them more suited to high-dimensional inputs like images. The main contribution of our work is the construction of an inter-domain inducing…

Motivation: In a predictive modeling setting, if sufficient details of the system behavior are known, one can build and use a simulation for making predictions. When sufficient system details are not known, one typically turns to machine…

We consider a Gaussian process formulation of the multiple kernel learning problem. The goal is to select the convex combination of kernel matrices that best explains the data and by doing so improve the generalisation on unseen data.…

The Gaussian kernel is a very popular kernel function used in many machine learning algorithms, especially in support vector machines (SVMs). It is more often used than polynomial kernels when learning from nonlinear datasets, and is…

In this paper, we present a comprehensive analysis of the posterior covariance field in Gaussian processes, with applications to the posterior covariance matrix. The analysis is based on the Gaussian prior covariance but the approach also…

Computer models are used as a way to explore complex physical systems. Stationary Gaussian process emulators, with their accompanying uncertainty quantification, are popular surrogates for computer models. However, many computer models are…

Despite the increasing importance of stochastic processes on linear networks and graphs, current literature on multivariate (vector-valued) Gaussian random fields on metric graphs is elusive. This paper challenges several aspects related to…

Capsule Networks attempt to represent patterns in images in a way that preserves hierarchical spatial relationships. Additionally, research has demonstrated that these techniques may be robust against adversarial perturbations. We present…

In the univariate setting, using the kernel spectral representation is an appealing approach for generating stationary covariance functions. However, performing the same task for multiple-output Gaussian processes is substantially more…

A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…

Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…

Gaussian processes provide a powerful probabilistic kernel learning framework, which allows learning high quality nonparametric regression models via methods such as Gaussian process regression. Nevertheless, the learning phase of Gaussian…

The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose…

The high efficiency of a recently proposed method for computing with Gaussian processes relies on expanding a (translationally invariant) covariance kernel into complex exponentials, with frequencies lying on a Cartesian equispaced grid.…

This work presents a family of parsimonious Gaussian process models which allow to build, from a finite sample, a model-based classifier in an infinite dimensional space. The proposed parsimonious models are obtained by constraining the…

Gaussian processes provide a flexible, non-parametric framework for the approximation of functions in high-dimensional spaces. The covariance kernel is the main engine of Gaussian processes, incorporating correlations that underpin the…

Kernel based methods including Gaussian process regression (GPR) and generally kernel ridge regression (KRR) have been finding increasing use in computational chemistry, including the fitting of potential energy surfaces and density…