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Bayesian optimal experiments that maximize the information gained from collected data are critical to efficiently identify behavioral models. We extend a seminal method for designing Bayesian optimal experiments by introducing two…

Applications · Statistics 2025-03-19 Stefano Balietti , Brennan Klein , Christoph Riedl

In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…

Numerical Analysis · Mathematics 2025-03-10 Jing Li , Yifeng Xu , Shengfeng Zhu

Optimal designs are usually model-dependent and likely to be sub-optimal if the postulated model is not correctly specified. In practice, it is common that a researcher has a list of candidate models at hand and a design has to be found…

Statistics Theory · Mathematics 2023-03-29 Mingyao Ai , Holger Dette , Zhengfu Liu , Jun Yu

We present novel algorithms for design and design space exploration. The designs discovered by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified…

Artificial Intelligence · Computer Science 2021-02-02 Alexander Feldman , Johan de Kleer , Ion Matei

We propose an algorithm for Bayesian functional optimisation - that is, finding the function to optimise a process - guided by experimenter beliefs and intuitions regarding the expected characteristics (length-scale, smoothness, cyclicity…

Machine Learning · Computer Science 2020-09-09 Alistair Shilton , Sunil Gupta , Santu Rana , Svetha Venkatesh

Performing optimal Bayesian design for discriminating between competing models is computationally intensive as it involves estimating posterior model probabilities for thousands of simulated datasets. This issue is compounded further when…

Methodology · Statistics 2022-04-07 Markus Hainy , David J. Price , Olivier Restif , Christopher Drovandi

In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of $O(n^{-1/5})$ for…

Optimization and Control · Mathematics 2021-09-02 Miklos Rasonyi , Kinga Tikosi

A Bayesian design is given by maximising an expected utility over a design space. The utility is chosen to represent the aim of the experiment and its expectation is taken with respect to all unknowns: responses, parameters and/or models.…

Methodology · Statistics 2019-01-16 Antony M. Overstall , James M. McGree

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

Machine Learning · Computer Science 2020-08-26 Burak Çakmak , Manfred Opper

Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…

Numerical Analysis · Mathematics 2017-08-28 Sou-Cheng T. Choi , Yuhan Ding , Fred J. Hickernell , Xin Tong

A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian…

Computational Physics · Physics 2013-05-14 Benedict Leimkuhler , Charles Matthews

Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal…

Machine Learning · Computer Science 2025-03-25 Xubo Yue , Raed Al Kontar , Albert S. Berahas , Yang Liu , Blake N. Johnson

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…

Machine Learning · Computer Science 2022-10-21 Noble Kennamer , Steven Walton , Alexander Ihler

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve…

Statistics Theory · Mathematics 2017-03-07 Yohann De Castro , F Gamboa , D Henrion , R Hess , J. -B Lasserre

In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…

Optimization and Control · Mathematics 2024-03-25 Chanwoo Park , Ernest K. Ryu

Suppose an online platform wants to compare a treatment and control policy, e.g., two different matching algorithms in a ridesharing system, or two different inventory management algorithms in an online retail site. Standard randomized…

Methodology · Statistics 2022-12-27 Peter Glynn , Ramesh Johari , Mohammad Rasouli

We propose a novel two-stage subsampling algorithm based on optimal design principles. In the first stage, we use a density-based clustering algorithm to identify an approximating design space for the predictors from an initial subsample.…

Methodology · Statistics 2024-03-20 Subhadra Dasgupta , Holger Dette

Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this…

Machine Learning · Statistics 2024-03-11 Shouri Hu , Jiawei Li , Zhibo Cai

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 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…

Machine Learning · Statistics 2017-11-15 Zeyuan Allen-Zhu , Yuanzhi Li , Aarti Singh , Yining Wang