Related papers: A Low Rank Gaussian Process Prediction Model for V…

The canonical technique for nonlinear modeling of spatial/point-referenced data is known as kriging in geostatistics, and as Gaussian Process (GP) regression for surrogate modeling and statistical learning. This article reviews many…

In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…

In the context of Gaussian Process Regression or Kriging, we propose a full-Bayesian solution to deal with hyperparameters of the covariance function. This solution can be extended to the Trans-Gaussian Kriging framework, which makes it…

We introduce a scalable Gaussian process (GP) framework with deep product kernels for data-driven learning of parametrized spatio-temporal fields over fixed or parameter-dependent domains. The proposed framework learns a continuous…

High-dimensional complex multi-parameter problems are prevalent in engineering, exceeding the capabilities of traditional surrogate models designed for low/medium-dimensional problems. These models face the curse of dimensionality,…

In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…

Stochastic kriging is a popular technique for simulation metamodeling due to its exibility and analytical tractability. Its computational bottleneck is the inversion of a covariance matrix, which takes $O(n^3)$ time in general and becomes…

Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…

Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…

For geospatial modelling and mapping tasks, variants of kriging - the spatial interpolation technique developed by South African mining engineer Danie Krige - have long been regarded as the established geostatistical methods. However,…

Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and…

Kriging (or Gaussian process regression) is a popular machine learning method for its flexibility and closed-form prediction expressions. However, one of the key challenges in applying kriging to engineering systems is that the available…

This paper presents a method for building a preconditioner for a kernel ridge regression problem, where the preconditioner is not only effective in its ability to reduce the condition number substantially, but also efficient in its…

Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly…

The Gaussian process is an indispensable tool for spatial data analysts. The onset of the "big data" era, however, has lead to the traditional Gaussian process being computationally infeasible for modern spatial data. As such, various…

This work investigates the prediction performance of the kriging predictors. We derive some error bounds for the prediction error in terms of non-asymptotic probability under the uniform metric and $L_p$ metrics when the spectral densities…

With computational models becoming more expensive and complex, surrogate models have gained increasing attention in many scientific disciplines and are often necessary to conduct sensitivity studies, parameter optimization etc. In the…

Low-rank approximation of a matrix by means of structured random sampling has been consistently efficient in its extensive empirical studies around the globe, but adequate formal support for this empirical phenomenon has been missing so…

In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…

Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…