Related papers: G-optimal grid designs for kriging models
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
We consider the general performance of the difference-in-means estimator in an equally-allocated two-arm randomized experiment under common experimental endpoints such as continuous (regression), incidence, proportion, count and uncensored…
We analyze the performance of graph neural network (GNN) architectures from the perspective of random graph theory. Our approach promises to complement existing lenses on GNN analysis, such as combinatorial expressive power and worst-case…
The integration of renewable energy sources and distributed generation in the power system calls for fast and reliable predictions of grid dynamics to achieve efficient control and ensure stability. In this work, we present a novel…
The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency…
We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…
The reconstruction of interaction networks between random events is a critical problem arising from statistical physics and politics, sociology, biology, psychology, and beyond. The Ising model lays the foundation for this reconstruction…
We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…
For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…
In this paper, we discuss two grid-quality measures, F- and G-measures, in relation to iterative convergence of an implicit unstructured-grid Navier-Stokes solver. The F-measure is a lower bound of a least-squares gradient, which is a…
We consider the problem of efficient statistical inference for comparing two regression curves estimated from two samples of dependent measurements. Based on a representation of the best pair of linear unbiased estimators in continuous time…
Gradient-enhanced Kriging (GE-Kriging) is a well-established surrogate modelling technique for approximating expensive computational models. However, it tends to get impractical for high-dimensional problems due to the size of the inherent…
The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state-of-the-art works mostly apply to design criteria on the estimates of regression coefficients.…
Parallel multigrid is widely used as preconditioners in solving large-scale sparse linear systems. However, the current multigrid library still needs more satisfactory performance for structured grid problems regarding speed and…
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…
In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…
Layout designs are encountered in a variety of fields. For problems with many design degrees of freedom, efficiency of design methods becomes a major concern. In recent years, machine learning methods such as artificial neural networks have…
Alphabetic optimality criteria, such as the $D$, $A$, and $I$ criteria, require specifying a model to select optimal designs. They are not model free and the optimal designs selected by them are not robust to model uncertainty. Recently,…
We consider performing simulation experiments in the presence of covariates. Here, covariates refer to some input information other than system designs to the simulation model that can also affect the system performance. To make decisions,…
Experimental designs for a generalized linear model (GLM) often depend on the specification of the model, including the link function, the predictors, and unknown parameters, such as the regression coefficients. To deal with uncertainties…