Related papers: Uncertainty Quantification and Experimental Design…

The vast quantity of information brought by big data as well as the evolving computer hardware encourages success stories in the machine learning community. In the meanwhile, it poses challenges for the Gaussian process (GP) regression, a…

Gaussian Process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset…

In many areas of the observational and experimental sciences data is scarce. Data observation in high-energy astrophysics is disrupted by celestial occlusions and limited telescope time while data derived from laboratory experiments in…

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior,…

Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…

Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…

Physical systems can often be described via a continuous-time dynamical system. In practice, the true system is often unknown and has to be learned from measurement data. Since data is typically collected in discrete time, e.g. by sensors,…

Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…

Gaussian processes are a powerful framework for uncertainty-aware function approximation and sequential decision-making. Unfortunately, their classical formulation does not scale gracefully to large amounts of data and modern hardware for…

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…

Sparse variational approximations allow for principled and scalable inference in Gaussian Process (GP) models. In settings where several GPs are part of the generative model, theses GPs are a posteriori coupled. For many applications such…

Gaussian Processes are widely used for regression tasks. A known limitation in the application of Gaussian Processes to regression tasks is that the computation of the solution requires performing a matrix inversion. The solution also…

Prior beliefs about the latent function to shape inductive biases can be incorporated into a Gaussian Process (GP) via the kernel. However, beyond kernel choices, the decision-making process of GP models remains poorly understood. In this…

The incomplete sampling of data in complex polarization measurements from radio telescopes negatively affects both the rotation measure (RM) transfer function and the Faraday depth spectra derived from these data. Such gaps in polarization…

Groundwater flow modeling is commonly used to calculate groundwater heads, estimate groundwater flow paths and travel times, and provide insights into solute transport processes within an aquifer. However, the values of input parameters…

While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…

Inference for GP models with non-Gaussian noises is computationally expensive when dealing with large datasets. Many recent inference methods approximate the posterior distribution with a simpler distribution defined on a small number of…

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…

Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. We provide Gaussian process models based on pseudo-likelihood approximation to perform sequence labeling. Gaussian…

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,…