Related papers: Optimal designs for rational function regression
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.…
Let $P = \{p(i)\}$ be a measure of strictly positive probabilities on the set of nonnegative integers. Although the countable number of inputs prevents usage of the Huffman algorithm, there are nontrivial $P$ for which known methods find a…
Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…
This paper describes the R package fdesigns that implements a methodology for identifying Bayesian optimal experimental designs for models whose factor settings are functions, known as profile factors. This type of experiments which involve…
We study how to construct compressed datasets that suffice to recover optimal decisions in linear programs with an unknown cost vector $c$ lying in a prior set $\mathcal{C}$. Recent work by Bennouna et al. provides an exact geometric…
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
We address the computational efficiency in solving the A-optimal Bayesian design of experiments problems for which the observational map is based on partial differential equations and, consequently, is computationally expensive to evaluate.…
A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
We consider the problem of optimizing a nonlinear objective function over a weighted independence system presented by a linear-optimization oracle. We provide a polynomial-time algorithm that determines an r-best solution for nonlinear…
In experimental design, we are given a large collection of vectors, each with a hidden response value that we assume derives from an underlying linear model, and we wish to pick a small subset of the vectors such that querying the…
Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…
Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while…
We address optimization of nonlinear functions of the form $f(Wx)$, where $f:\R^d\to \R$ is a nonlinear function, $W$ is a $d\times n$ matrix, and feasible $x$ are in some large finite set $F$ of integer points in $\R^n$. One motivation is…
The design of specified nonlinear mechanical responses into a structure or material is a highly sought after capability, which would have a significant impact in areas such as wave tailoring in metamaterials, impact mitigation, soft…
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…
We propose a class of subspace ascent methods for computing optimal approximate designs that covers both existing as well as new and more efficient algorithms. Within this class of methods, we construct a simple, randomized exchange…
This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…
In experimental design, we are given $n$ vectors in $d$ dimensions, and our goal is to select $k\ll n$ of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have…