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A fundamental task in numerical computation is the solution of large linear systems. The conjugate gradient method is an iterative method which offers rapid convergence to the solution, particularly when an effective preconditioner is…
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…
Gaussian processes (GPs) are ubiquitous tools for modeling and predicting continuous processes in physical and engineering sciences. This is partly due to the fact that one may employ a Gaussian process as an interpolator while facilitating…
Sparse Gaussian processes and various extensions thereof are enabled through inducing points, that simultaneously bottleneck the predictive capacity and act as the main contributor towards model complexity. However, the number of inducing…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
The estimation of small probabilities of failure from computer simulations is a classical problem in engineering, and the Subset Simulation algorithm proposed by Au & Beck (Prob. Eng. Mech., 2001) has become one of the most popular method…
We introduce a novel edge tracing algorithm using Gaussian process regression. Our edge-based segmentation algorithm models an edge of interest using Gaussian process regression and iteratively searches the image for edge pixels in a…
The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…
Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond…
This paper presents a kriging method for spatial prediction of temporal intensity functions, for situations where a temporal point process is observed at different spatial locations. Assuming that several replications of the processes are…
This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian…
For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are…
Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…
Nested sampling (NS) is a popular algorithm for Bayesian computation. We investigate statistical errors in NS both analytically and numerically. We show two analytic results. First, we show that the leading terms in Skilling's expression…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
We present a numerical framework for computing nested quadrature rules for various weight functions. The well-known Kronrod method extends the Gauss-Legendre quadrature by adding new optimal nodes to the existing Gauss nodes for integration…
We propose a three-step divide-and-conquer strategy within the Bayesian paradigm that delivers massive scalability for any spatial process model. We partition the data into a large number of subsets, apply a readily available Bayesian…
Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis…
We address the issue of knots selection for Gaussian predictive process methodology. Predictive process approximation provides an effective solution to the cubic order computational complexity of Gaussian process models. This approximation…
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…