Related papers: Gaussian Process Regression as a Sustainable Data-…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Efficient exploration of parameter spaces is crucial to extract physical information about the Epoch of Reionization from various observational probes. To this end, we propose a fast technique based on Gaussian Process Regression (GPR)…
In spatial statistics, a common method for prediction over a Gaussian random field (GRF) is maximum likelihood estimation combined with kriging. For massive data sets, kriging is computationally intensive, both in terms of CPU time and…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
While the analysis of airborne laser scanning (ALS) data often provides reliable estimates for certain forest stand attributes -- such as total volume or basal area -- there is still room for improvement, especially in estimating…
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…
In this work we consider Bayesian inference problems with intractable likelihood functions. We present a method to compute an approximate of the posterior with a limited number of model simulations. The method features an inverse Gaussian…
Gaussian processes (GPs) are a Bayesian machine learning approach widely used to construct surrogate models for the uncertainty quantification of computer simulation codes in industrial applications. It provides both a mean predictor and an…
Sparse variational Gaussian processes (GPs) construct tractable posterior approximations to GP models. At the core of these methods is the assumption that the true posterior distribution over training function values ${\bf f}$ and inducing…
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications. Such scenarios demand that GP decisions are not only accurate, but also robust to perturbations. In this…
We apply Gaussian process (GP) regression, which provides a powerful non-parametric probabilistic method of relating inputs to outputs, to survival data consisting of time-to-event and covariate measurements. In this context, the covariates…
This work is concerned with the convergence of Gaussian process regression. A particular focus is on hierarchical Gaussian process regression, where hyper-parameters appearing in the mean and covariance structure of the Gaussian process…
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…
Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have…
Gaussian Processes (GPs) are widely recognized as powerful non-parametric models for regression and classification. Traditional GP frameworks predominantly operate under the assumption that the inputs are either accurately known or subject…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
Hyper-parameter optimization remains as the core issue of Gaussian process (GP) for machine learning nowadays. The benchmark method using maximum likelihood (ML) estimation and gradient descent (GD) is impractical for processing big data…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…
The combination of inducing point methods with stochastic variational inference has enabled approximate Gaussian Process (GP) inference on large datasets. Unfortunately, the resulting predictive distributions often exhibit substantially…