Related papers: Single Nugget Kriging
Kriging is a widely employed technique, in particular for computer experiments, in machine learning or in geostatistics. An important challenge for Kriging is the computational burden when the data set is large. This article focuses on a…
Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict…
This work falls within the context of predicting the value of a real function at some input locations given a limited number of observations of this function. The Kriging interpolation technique (or Gaussian process regression) is often…
To obtain more accurate model parameters and improve prediction accuracy, we proposed a regularized Kriging model that penalizes the hyperparameter theta in the Gaussian stochastic process, termed the Theta-regularized Kriging. We derived…
Exact Kriging and conditional simulation (CS) for uncertainty quantification are computationally infeasible for modern spatial analyses with large numbers of observations and dense prediction grids. We present a rapid approximation to the…
Kriging and Gaussian Process Regression are statistical methods that allow predicting the outcome of a random process or a random field by using a sample of correlated observations. In other words, the random process or random field is…
Kriging or Gaussian Process Regression is applied in many fields as a non-linear regression model as well as a surrogate model in the field of evolutionary computation. However, the computational and space complexity of Kriging, that is…
In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…
In the Big Data era, with the ubiquity of geolocation sensors in particular, massive datasets exhibiting a possibly complex spatial dependence structure are becoming increasingly available. In this context, the standard probabilistic theory…
Spatial prediction requires expensive computation to invert the spatial covariance matrix it depends on and also has considerable storage needs. This work concentrates on computationally efficient algorithms for prediction using very large…
Spatial prediction in an arbitrary location, based on a spatial set of observations, is usually performed by Kriging, being the best linear unbiased predictor (BLUP) in a least-square sense. In order to predict a continuous surface over a…
This article proposes a new kriging that has a rational form. It is shown that the generalized least squares estimate of the mean from rational kriging is much more well behaved than that from ordinary kriging. Parameter estimation and…
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…
Kriging-based surrogate models have become very popular during the last decades to approximate a computer code output from few simulations. In practical applications, it is very common to sequentially add new simulations to obtain more…
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…
Kriging is the predominant method used for spatial prediction, but relies on the assumption that predictions are linear combinations of the observations. Kriging often also relies on additional assumptions such as normality and…
Gaussian process (GP) models are effective non-linear models for numerous scientific applications. However, computation of their hyperparameters can be difficult when there is a large number of training observations (n) due to the O(n^3)…
The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a…
Combination of low-tensor rank techniques and the Fast Fourier transform (FFT) based methods had turned out to be prominent in accelerating various statistical operations such as Kriging, computing conditional covariance, geostatistical…
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…