Related papers: Explaining and Connecting Kriging with Gaussian Pr…
Assume that a Gaussian process $\xi$ is predicted from $n$ pointwise observations by intrinsic Kriging and that the volume of the excursion set of $\xi$ above a given threshold $u$ is approximated by the volume of the predictor. The first…
Consider a family $Z=\{\boldsymbol{x_{i}},y_{i}$,$1\leq i\leq N\}$ of $N$ pairs of vectors $\boldsymbol{x_{i}} \in \mathbb{R}^d$ and scalars $y_{i}$ that we aim to predict for a new sample vector $\mathbf{x}_0$. Kriging models $y$ as a sum…
Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. One way to preserve this imprecision in a geostatistical mapping framework is to characterize the measurements as intervals rather…
In this paper, we investigate Gaussian process modeling with input location error, where the inputs are corrupted by noise. Here, the best linear unbiased predictor for two cases is considered, according to whether there is noise at the…
In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse…
In this work, we investigate Gaussian process regression used to recover a function based on noisy observations. We derive upper and lower error bounds for Gaussian process regression with possibly misspecified correlation functions. The…
Gaussian processes offer a flexible kernel method for regression. While Gaussian processes have many useful theoretical properties and have proven practically useful, they suffer from poor scaling in the number of observations. In…
Machine learning and geostatistics are two fundamentally different frameworks for predicting and spatially mapping soil properties. Geostatistics leverages the spatial structure of soil properties, while machine learning captures the…
Kriging is a fundamental tool for spatial prediction, but its computational complexity of $O(N^3)$ becomes prohibitive for large datasets. While local kriging using $K$-nearest neighbors addresses this issue, the selection of $K$ typically…
Gaussian process regression (GPR) is a popular nonparametric Bayesian method that provides predictive uncertainty estimates and is widely used in safety-critical applications. While prior research has introduced various uncertainty bounds,…
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and…
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales…
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…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
The hedonic approach based on a regression model has been widely adopted for the prediction of real estate property price and rent. In particular, a spatial regression technique called Kriging, a method of interpolation that was advanced in…
This work addresses the interpolation of probability measures within a spatial statistics framework. We develop a Kriging approach in the Wasserstein space, leveraging the quantile function representation of the one-dimensional Wasserstein…
Stochastic kriging is a popular metamodeling technique for representing the unknown response surface of a simulation model. However, the simulation model may be inadequate in the sense that there may be a non-negligible discrepancy between…
The increased demand for online prediction and the growing availability of large data sets drives the need for computationally efficient models. While exact Gaussian process regression shows various favorable theoretical properties…
Gaussian process regression (GPR) is a fundamental model used in machine learning. Owing to its accurate prediction with uncertainty and versatility in handling various data structures via kernels, GPR has been successfully used in various…
Gaussian Process Regression (GPR) is a popular regression method, which unlike most Machine Learning techniques, provides estimates of uncertainty for its predictions. These uncertainty estimates however, are based on the assumption that…