Related papers: Random generation of optimal saturated designs
In this work we focus on saturated $D$-optimal designs. Using recent results, we identify $D$-optimal designs with the solutions of an optimization problem with linear constraints. We introduce new objective functions based on the geometric…
In this paper, we propose two simple yet efficient computational algorithms to obtain approximate optimal designs for multi-dimensional linear regression on a large variety of design spaces. We focus on the two commonly used optimal…
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…
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…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
Algorithm design is a laborious process and often requires many iterations of ideation and validation. In this paper, we explore automating algorithm design and present a method to learn an optimization algorithm, which we believe to be the…
Algorithms for machine learning-guided design, or design algorithms, use machine learning-based predictions to propose novel objects with desired property values. Given a new design task -- for example, to design novel proteins with high…
We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann. Statist.…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…
Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully…
Design of experiments, random search, initialization of population-based methods, or sampling inside an epoch of an evolutionary algorithm use a sample drawn according to some probability distribution for approximating the location of an…
Randomized saturation designs are a family of designs which assign a possibly different treatment proportion to each cluster of a population at random. As a result, they generalize the well-known (stratified) completely randomized designs…
We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While…
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…
Systems with both quantitative and qualitative responses are widely encountered in many applications. Design of experiment methods are needed when experiments are conducted to study such systems. Classic experimental design methods are…
Modern advanced manufacturing and advanced materials design often require searches of relatively high-dimensional process control parameter spaces for settings that result in optimal structure, property, and performance parameters. The…
Experimental design is a classical statistics problem and its aim is to estimate an unknown $m$-dimensional vector $\beta$ from linear measurements where a Gaussian noise is introduced in each measurement. For the combinatorial experimental…
Topology Optimization seeks to find the best design that satisfies a set of constraints while maximizing system performance. Traditional iterative optimization methods like SIMP can be computationally expensive and get stuck in local…