Related papers: Efficient Gaussian process learning via subspace p…

In decision-making systems, it is important to have classifiers that have calibrated uncertainties, with an optimisation objective that can be used for automated model selection and training. Gaussian processes (GPs) provide uncertainty…

We explore the performance of a statistical learning technique based on Gaussian Process (GP) regression as an efficient non-parametric method for constructing multi-dimensional potential energy surfaces (PES) for polyatomic molecules.…

A generalized Gaussian process model (GGPM) is a unifying framework that encompasses many existing Gaussian process (GP) models, such as GP regression, classification, and counting. In the GGPM framework, the observation likelihood of the…

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing…

This article deals with random projections applied as a data reduction technique for Bayesian regression analysis. We show sufficient conditions under which the entire $d$-dimensional distribution is approximately preserved under random…

The Gaussian splatting methods are getting popular. However, their loss function only contains the $\ell_1$ norm and the structural similarity between the rendered and input images, without considering the edges in these images. It is…

This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify…

Data-driven approaches achieve remarkable results for the modeling of complex dynamics based on collected data. However, these models often neglect basic physical principles which determine the behavior of any real-world system. This…

This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across…

Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models…

In this work, we propose a non-parametric probabilistic load flow (NP-PLF) technique based on the Gaussian Process (GP) learning to understand the power system behavior under uncertainty for better operational decisions. The technique can…

In this paper, we explore the application of Gaussian Processes (GPs) for predicting mean-reverting time series with an underlying structure, using relatively unexplored functional and augmented data structures. While many conventional…

Probabilistic models are often used to make predictions in regions of the data space where no observations are available, but it is not always clear whether such predictions are well-informed by previously seen data. In this paper, we…

In our previous work, we designed a systematic policy to prioritize sampling locations to lead significant accuracy improvement in spatial interpolation by using the prediction uncertainty of Gaussian Process Regression (GPR) as "attraction…

Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the…

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…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

In complex and unknown processes, global models are initially generated over the entire experimental space but often fail to provide accurate predictions in local areas. A common approach is to use local models, which requires partitioning…

This paper presents an approach for constrained Gaussian Process (GP) regression where we assume that a set of linear transformations of the process are bounded. It is motivated by machine learning applications for high-consequence…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…