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Recently, machine learning has been introduced in the inverse design of physical devices, i.e., the automatic generation of device geometries for a desired physical response. In particular, generative adversarial networks have been proposed…

Optics · Physics 2025-02-18 Timo Gahlmann , Philippe Tassin

In this paper optimal designs for regression problems with spherical predictors of arbitrary dimension are considered. Our work is motivated by applications in material sciences, where crystallographic textures such as the missorientation…

Statistics Theory · Mathematics 2017-10-31 Holger Dette , Maria Konstantinou , Kirsten Schorning , Josua Gösmann

Modeling real processes often results in several suitable models. In order to be able to distinguish, or discriminate, which model best represents a phenomenon, one is interested, e.g., in so-called T-optimal designs. These consist of the…

Optimization and Control · Mathematics 2022-08-30 David Mogalle , Philipp Seufert , Jan Schwientek , Michael Bortz , Karl-Heinz Küfer

The theory of optimal design of experiments has been traditionally developed on an Euclidean space. In this paper, new theoretical results and an algorithm for finding the optimal design of an experiment located on a Riemannian manifold are…

Statistics Theory · Mathematics 2023-02-03 Hang Li , Enrique Del Castillo

The selection of smoothing parameter is central to the estimation of penalized splines. The best value of the smoothing parameter is often the one that optimizes a smoothness selection criterion, such as generalized cross-validation error…

Methodology · Statistics 2022-12-12 Zheyuan Li , Jiguo Cao

A unified framework to derive optimized compact schemes for a uniform grid is presented. The optimal scheme coefficients are determined analytically by solving an optimization problem to minimize the spectral error subject to equality…

Numerical Analysis · Mathematics 2019-12-17 Vedang M. Deshpande , Raktim Bhattacharya , Diego A. Donzis

We consider the problem of designing experiments for the comparison of two regression curves describing the relation between a predictor and a response in two groups, where the data between and within the group may be dependent. In order to…

Statistics Theory · Mathematics 2021-01-15 Kirsten Schorning , Holger Dette

We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…

Numerical Analysis · Mathematics 2020-04-02 Elizabeth Herman , Alen Alexanderian , Arvind K. Saibaba

Sequential Bayesian optimal experimental design (SBOED) for PDE-governed inverse problems is computationally challenging, especially for infinite-dimensional random field parameters. High-fidelity approaches require repeated forward and…

Optimization and Control · Mathematics 2026-01-12 Kaichen Shen , Peng Chen

Structured prediction tasks in machine learning involve the simultaneous prediction of multiple labels. This is typically done by maximizing a score function on the space of labels, which decomposes as a sum of pairwise elements, each…

Machine Learning · Computer Science 2014-09-23 Amir Globerson , Tim Roughgarden , David Sontag , Cafer Yildirim

In this paper we consider the problem of constructing $T$-optimal discriminating designs for Fourier regression models. We provide explicit solutions of the optimal design problem for discriminating between two Fourier regression models,…

Methodology · Statistics 2015-12-24 Holger Dette , Viatcheslav B. Melas , Petr Shpilev

Many geosciences data are imprecise due to various limitations and uncertainties in the measuring process. One way to preserve this imprecision in a geostatistical mapping framework is to characterize the measurements as intervals rather…

Methodology · Statistics 2019-11-22 Brennan Bean , Yan Sun , Marc Maguire

There are different MV grid concepts with regard to mode of operation and protection system layout. The increasing installation of DG raises the question if the currently used concepts are still optimal for future power systems. We present…

Computational Engineering, Finance, and Science · Computer Science 2018-02-06 Leon Thurner , Alexander Scheidler , Alexander Probst , Martin Braun

We study the optimal design problem under second-order least squares estimation which is known to outperform ordinary least squares estimation when the error distribution is asymmetric. First, a general approximate theory is developed,…

Statistics Theory · Mathematics 2014-05-14 Mausumi Bose , Rahul Mukerjee

We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant…

Computation · Statistics 2023-02-24 Samuel I Watson , Yi Pan

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…

Methodology · Statistics 2025-04-16 V. Roshan Joseph

Bayesian optimality criteria provide a robust design strategy to parameter misspecification. We develop an approximate design theory for Bayesian $D$-optimality for non-linear regression models with covariates subject to measurement errors.…

Methodology · Statistics 2016-05-16 Maria Konstantinou , Holger Dette

Different from a typical independent identically distributed (IID) element assumption, this paper studies the estimation of IID row random matrix for the generalized linear model constructed by a linear mixing space and a row-wise mapping…

Information Theory · Computer Science 2021-09-28 Qiuyun Zou , Hongwen Yang

We investigate the impact of the input dimension on the generalization error in generative adversarial networks (GANs). In particular, we first provide both theoretical and practical evidence to validate the existence of an optimal input…

Machine Learning · Computer Science 2024-05-08 Zhiyao Tan , Ling Zhou , Huazhen Lin

Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets,…

Methodology · Statistics 2021-07-20 Karl T. Pazdernik , Ranjan Maitra