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Related papers: Approximation Algorithms for D-optimal Design

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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,…

Computation · Statistics 2016-04-14 Chang-Yun Lin

In multi-response regression models, the error covariance matrix is never known in practice. Thus, there is a need for optimal designs which are robust against possible misspecification of the error covariance matrix. In this paper, we…

Methodology · Statistics 2019-10-03 Lucy L. Gao , Julie Zhou

Robust covariance estimation is the following, well-studied problem in high dimensional statistics: given $N$ samples from a $d$-dimensional Gaussian $\mathcal{N}(\boldsymbol{0}, \Sigma)$, but where an $\varepsilon$-fraction of the samples…

Data Structures and Algorithms · Computer Science 2020-06-25 Jerry Li , Guanghao Ye

A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific…

Optimization and Control · Mathematics 2015-03-17 Dominik Skanda , Dirk Lebiedz

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…

Optimization and Control · Mathematics 2026-04-21 Jochen Schmid , Philipp Seufert , Jan Schwientek , Tobias Seidel , Karl-Heinz Küfer

Efficient algorithms for searching for optimal saturated designs are widely available. They maximize a given efficiency measure (such as D-optimality) and provide an optimum design. Nevertheless, they do not guarantee a \emph{global}…

Computation · Statistics 2013-03-29 Roberto Fontana

Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…

Methodology · Statistics 2021-01-18 Philipp Seufert , Jan Schwientek , Michael Bortz

We present a unified deterministic approach for experimental design problems using the method of interlacing polynomials. Our framework recovers the best-known approximation guarantees for the well-studied D/A/E-design problems with simple…

Data Structures and Algorithms · Computer Science 2024-10-16 Lap Chi Lau , Robert Wang , Hong Zhou

Randomized approximation algorithms for many #P-complete problems (such as the partition function of a Gibbs distribution, the volume of a convex body, the permanent of a $\{0,1\}$-matrix, and many others) reduce to creating random…

Computation · Statistics 2017-06-30 Mark Huber

We develop a set of algorithms to solve a broad class of Design of Experiment (DoE) problems efficiently. Specifically, we consider problems in which one must choose a subset of polymers to test in experiments such that the learning of the…

Quantitative Methods · Quantitative Biology 2024-08-06 Swagatam Mukhopadhyay

Bayesian optimal design is considered for experiments where the response distribution depends on the solution to a system of non-linear ordinary differential equations. The motivation is an experiment to estimate parameters in the equations…

Methodology · Statistics 2019-05-02 Antony Overstall , David Woods , Ben Parker

In this paper, we address the problem of designing an experimental plan with both discrete and continuous factors under fairly general parametric statistical models. We propose a new algorithm, named ForLion, to search for locally optimal…

Computation · Statistics 2024-05-24 Yifei Huang , Keren Li , Abhyuday Mandal , Jie Yang

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

We consider the problem of obtaining D-optimal designs for factorial experiments with a binary response and $k$ qualitative factors each at two levels. We obtain a characterization for a design to be locally D-optimal. Based on this…

Statistics Theory · Mathematics 2015-03-19 Jie Yang , Abhyuday Mandal , Dibyen Majumdar

The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general…

Machine Learning · Statistics 2012-12-04 Xun Huan , Youssef M. Marzouk

Optimal experimental design (OED) is the general formalism of sensor placement and decisions about the data collection strategy for engineered or natural experiments. This approach is prevalent in many critical fields such as battery…

Optimization and Control · Mathematics 2022-06-28 Ahmed Attia , Emil Constantinescu

One of the most common problems in statistical experimentation is computing D-optimal designs on large finite candidate sets. While optimal approximate (i.e., infinite-sample) designs can be efficiently computed using convex methods,…

Computation · Statistics 2026-01-12 Radoslav Harman , Samuel Rosa

Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a…

Statistics Theory · Mathematics 2021-01-01 Geovani Rizk , Igor Colin , Albert Thomas , Moez Draief

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

Optimization and Control · Mathematics 2024-06-04 Jochen Schmid , Philipp Seufert , Michael Bortz

We study the fundamental problem of learning the parameters of a high-dimensional Gaussian in the presence of noise -- where an $\varepsilon$-fraction of our samples were chosen by an adversary. We give robust estimators that achieve…

Data Structures and Algorithms · Computer Science 2017-11-07 Ilias Diakonikolas , Gautam Kamath , Daniel M. Kane , Jerry Li , Ankur Moitra , Alistair Stewart