Related papers: Calculation of Discrepancy Measures and Applicatio…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…
Anomaly detection has important applications in biosurveilance and environmental monitoring. When comparing measured data to data drawn from a baseline distribution, merely, finding clusters in the measured data may not actually represent…
Discrepancy measures how uniformly distributed a point set is with respect to a given set of ranges. There are two notions of discrepancy, namely continuous discrepancy and combinatorial discrepancy. Depending on the ranges, several…
Estimation of time delays from a noisy and gapped data is one of the simplest data analysis problems in astronomy by its formulation. But as history of real experiments show, the work with observed data sets can be quite complex and…
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…
Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set…
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
Motivated by applications in instance selection, we introduce the star discrepancy subset selection problem, which consists of finding a subset of m out of n points that minimizes the star discrepancy. First, we show that this problem is…
Building upon the exact methods presented in our earlier work [J. Complexity, 2022], we introduce a heuristic approach for the star discrepancy subset selection problem. The heuristic gradually improves the current-best subset by replacing…
Let P be a set of points in R^d, and let M be a function that maps any subset of P to a positive real number. We examine the problem of computing the exact mean and variance of M when a subset of points in P is selected according to a…
We propose simple schemes that can perfectly identify projective measurement apparatus secretly chosen from a finite set. Entanglements are used in these schemes both to make possible the perfect identification and to improve the efficiency…
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
We present a new method for detecting and correcting systematic errors in the distances to stars when both proper motions and line-of-sight velocities are available. The method, which is applicable for samples of 200 or more stars that have…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
Discrepancy is a well-known measure for the irregularity of the distribution of a point set. Point sets with small discrepancy are called low-discrepancy and are known to efficiently fill the space in a uniform manner. Low-discrepancy…
The construction of low-discrepancy sets, used for uniform sampling and numerical integration, has recently seen great improvements based on optimization and machine learning techniques. However, these methods are computationally expensive,…
The star discrepancy $D_N^*(\mathcal{P})$ is a quantitative measure for the irregularity of distribution of a finite point set $\mathcal{P}$ in the multi-dimensional unit cube which is intimately related to the integration error of…