Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples
M Gnewuch, N Hebbinghaus - The Annals of Applied Probability, 2021 - projecteuclid.org
We introduce a class of γ-negatively dependent random samples. We prove that this class
includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin …
includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin …
Calculation of discrepancy measures and applications
In this book chapter we survey known approaches and algorithms to compute discrepancy
measures of point sets. After providing an introduction which puts the calculation of …
measures of point sets. After providing an introduction which puts the calculation of …
An Empirical Evaluation of -Means Coresets
C Schwiegelshohn, OA Sheikh-Omar - arXiv preprint arXiv:2207.00966, 2022 - arxiv.org
Coresets are among the most popular paradigms for summarizing data. In particular, there
exist many high performance coresets for clustering problems such as $ k $-means in both …
exist many high performance coresets for clustering problems such as $ k $-means in both …
[HTML][HTML] Heuristic approaches to obtain low-discrepancy point sets via subset selection
Building upon the exact methods presented in our earlier work (2022)[5], we introduce a
heuristic approach for the star discrepancy subset selection problem. The heuristic gradually …
heuristic approach for the star discrepancy subset selection problem. The heuristic gradually …
Discrepancy, integration and tractability
A Hinrichs - Monte Carlo and Quasi-Monte Carlo Methods 2012, 2013 - Springer
The discrepancy function of a point distribution measures the deviation from the uniform
distribution. Different versions of the discrepancy function capture this deviation with respect …
distribution. Different versions of the discrepancy function capture this deviation with respect …
The limited blessing of low dimensionality: when 1-1/d is the best possible exponent for d-dimensional geometric problems
D Marx, A Sidiropoulos - Proceedings of the thirtieth annual symposium …, 2014 - dl.acm.org
We are studying d-dimensional geometric problems that have algorithms with 1− 1/d
appearing in the exponent of the running time, for example, in the form of 2n1− 1/d or nk1 …
appearing in the exponent of the running time, for example, in the form of 2n1− 1/d or nk1 …
Computing star discrepancies with numerical black-box optimization algorithms
F Clément, D Vermetten, J De Nobel… - Proceedings of the …, 2023 - dl.acm.org
The L∞ star discrepancy is a measure for the regularity of a finite set of points taken from [0,
1) d. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in …
1) d. Low discrepancy point sets are highly relevant for Quasi-Monte Carlo methods in …
[HTML][HTML] Star discrepancy subset selection: Problem formulation and efficient approaches for low dimensions
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 …
selection problem, which consists of finding a subset of m out of n points that minimizes the …
A new randomized algorithm to approximate the star discrepancy based on threshold accepting
M Gnewuch, M Wahlström, C Winzen - SIAM Journal on Numerical Analysis, 2012 - SIAM
We present a new algorithm for estimating the star discrepancy of arbitrary point sets. Similar
to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal …
to the algorithm for discrepancy approximation of Winker and Fang [SIAM J. Numer. Anal …