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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…

This paper examines experimental design procedures used to develop surrogates of computational models, exploring the interplay between experimental designs and approximation algorithms. We focus on two widely used approximation approaches,…

Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…

Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the…

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

We develop a Gaussian process framework for learning interaction kernels in multi-species interacting particle systems from trajectory data. Such systems provide a canonical setting for multiscale modeling, where simple microscopic…

A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…

Due to the increasing complexity of technical systems, accurate first principle models can often not be obtained. Supervised machine learning can mitigate this issue by inferring models from measurement data. Gaussian process regression is…

We develop a flexible Gaussian Process (GP) framework for learning the covariance structure of Age- and Year-specific mortality surfaces. Utilizing the additive and multiplicative structure of GP kernels, we design a genetic programming…

Gaussian process regression has proven very powerful in statistics, machine learning and inverse problems. A crucial aspect of the success of this methodology, in a wide range of applications to complex and real-world problems, is…

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…

Latent confounders---unobserved variables that influence both treatment and outcome---can bias estimates of causal effects. In some cases, these confounders are shared across observations, e.g. all students taking a course are influenced by…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

We propose a representation of Gaussian processes (GPs) based on powers of the integral operator defined by a kernel function, we call these stochastic processes integral Gaussian processes (IGPs). Sample paths from IGPs are functions…

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…

In this paper we introduce GP+, an open-source library for kernel-based learning via Gaussian processes (GPs) which are powerful statistical models that are completely characterized by their parametric covariance and mean functions. GP+ is…

Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e. the function spaces over…

Gaussian Processes (GP) are widely used for probabilistic modeling and inference for nonparametric regression. However, their computational complexity scales cubicly with the sample size rendering them unfeasible for large data sets. To…

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no…