Related papers: Wasserstein-type Gaussian Process Regressions for …

Numerical relativity (NR) enables the study of physics in strong and dynamical gravitational fields and provides predictions for the gravitational-wave signals produced by merging black holes. Despite the impressive accuracy of modern…

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…

In this article, we consider the general task of performing Gaussian process regression (GPR) on pointwise observations of solutions of the 3 dimensional homogeneous free space wave equation.In a recent article, we obtained promising…

Uncertainty quantification in neural networks through methods such as Dropout, Bayesian neural networks and Laplace approximations is either prone to underfitting or computationally demanding, rendering these approaches impractical for…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is 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,…

Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse…

In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…

Neural-net-induced Gaussian process (NNGP) regression inherits both the high expressivity of deep neural networks (deep NNs) as well as the uncertainty quantification property of Gaussian processes (GPs). We generalize the current NNGP to…

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 processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed…

The growing demand for accurate, efficient, and scalable solutions in computational mechanics highlights the need for advanced operator learning algorithms that can efficiently handle large datasets while providing reliable uncertainty…

Mechanistic simulation models are inverted against observations in order to gain inference on modeled processes. However, with the increasing ability to collect high resolution observations, these observations represent more patterns of…

The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…

Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design. While learning-based control has the potential to yield superior performance in…

Gaussian processes (GP) are widely used as a metamodel for emulating time-consuming computer codes. We focus on problems involving categorical inputs, with a potentially large number L of levels (typically several tens), partitioned in G <<…

We develop a fast variational approximation scheme for Gaussian process (GP) regression, where the spectrum of the covariance function is subjected to a sparse approximation. Our approach enables uncertainty in covariance function…

While Gaussian processes are a mainstay for various engineering and scientific applications, the uncertainty estimates don't satisfy frequentist guarantees and can be miscalibrated in practice. State-of-the-art approaches for designing…

Gaussian process (GP) is a powerful modeling method with applications in machine learning for various engineering and non-engineering fields. Despite numerous benefits of modeling using GPs, the computational complexity associated with GPs…