Related papers: Uniform Maximum Projection Designs for Computer Ex…
Optimal experimental design (OED) aims to choose the observations in an experiment to be as informative as possible, according to certain statistical criteria. In the linear case (when the observations depend linearly on the unknown…
Performing a computer experiment can be viewed as observing a mapping between the model parameters and the corresponding model outputs predicted by the computer model. In view of this, experimental design for computer experiments can be…
The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a…
In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
Computer experiments have become ubiquitous in science and engineering. Commonly, runs of these simulations demand considerable time and computing, making experimental design extremely important in gaining high quality information with…
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…
Maximum Mean Discrepancy (MMD) has been widely used in the areas of machine learning and statistics to quantify the distance between two distributions in the $p$-dimensional Euclidean space. The asymptotic property of the sample MMD has…
The variational inequality problem in finite-dimensional Euclidean space is addressed in this paper, and two inexact variants of the extragradient method are proposed to solve it. Instead of computing exact projections on the constraint…
Selecting prototypical examples from a source distribution to represent a target data distribution is a fundamental problem in machine learning. Existing subset selection methods often rely on implicit importance scores, which can be skewed…
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…
A common challenge in computer experiments and related fields is to efficiently explore the input space using a small number of samples, i.e., the experimental design problem. Much of the recent focus in the computer experiment literature,…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…
The two-layer computer simulators are commonly used to mimic multi-physics phenomena or systems. Usually, the outputs of the first-layer simulator (also called the inner simulator) are partial inputs of the second-layer simulator (also…
Designing messenger RNA (mRNA) sequences for a fixed target protein requires searching an exponentially large synonymous space while optimizing properties that affect stability and downstream performance. This is challenging because…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
The growing prevalence of high-dimensional data has fostered the development of multidimensional projection (MP) techniques, such as t-SNE, UMAP, and LAMP, for data visualization and exploration. However, conventional MP methods typically…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…