Related papers: On proportional volume sampling for experimental d…
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,…
Space filling designs are central to studying complex systems in various areas of science. They are used for obtaining an overall understanding of the behaviour of the response over the input space, model construction and uncertainty…
We consider a stochastic variational inequality (SVI) problem with a continuous and monotone mapping over a closed and convex set. In strongly monotone regimes, we present a variable sample-size averaging scheme (VS-Ave) that achieves a…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…
We extend our study of Motion Planning via Manifold Samples (MMS), a general algorithmic framework that combines geometric methods for the exact and complete analysis of low-dimensional configuration spaces with sampling-based approaches…
We introduce a principal support vector machine (PSVM) approach that can be used for both linear and nonlinear sufficient dimension reduction. The basic idea is to divide the response variables into slices and use a modified form of support…
Given a full rank matrix $X$ with more columns than rows, consider the task of estimating the pseudo inverse $X^+$ based on the pseudo inverse of a sampled subset of columns (of size at least the number of rows). We show that this is…
Sampling one or more effective solutions from large search spaces is a recurring idea in machine learning, and sequential optimization has become a popular solution. Typical examples include data summarization, sample mining for predictive…
We present an efficient method for computing A-optimal experimental designs for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we address the problem of optimizing the…
This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high dimensional…
Sampling from high dimensional distributions and volume approximation of convex bodies are fundamental operations that appear in optimization, finance, engineering, artificial intelligence and machine learning. In this paper we present…
Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…
For many important problems the quantity of interest is an unknown function of the parameters, which is a random vector with known statistics. Since the dependence of the output on this random vector is unknown, the challenge is to identify…
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…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
Recent findings by Jahn, T. Ullrich, Voigtlaender [10] relate non-linear sampling numbers for the square norm to quantities involving trigonometric best $m-$term approximation errors in the uniform norm. Here we establish new results for…
We revisit the classical problem of optimal experimental design (OED) under a new mathematical model grounded in a geometric motivation. Specifically, we introduce models based on elementary symmetric polynomials; these polynomials capture…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…