Related papers: Transforming the Challenge of Constructing Low-Dis…
Experimental designs intended to match arbitrary target distributions are typically constructed via a variable transformation of a uniform experimental design. The inverse distribution function is one such transformation. The discrepancy is…
In this article we survey recent results on the explicit construction of finite point sets and infinite sequences with optimal order of $\mathcal{L}_q$ discrepancy. In 1954 Roth proved a lower bound for the $\mathcal{L}_2$ discrepancy of…
The Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is one of the most successful examples of a derandomized evolution strategy. However, it still relies on randomly sampling offspring, which can be done via a uniform distribution…
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Fibonacci point set in the unit square. It was observed recently that this new characteristic allows us to obtain optimal rate…
Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…
The L_2-discrepancy measures the irregularity of the distribution of a finite point set. In this note we prove lower bounds for the L_2 discrepancy of arbitrary N-point sets. Our main focus is on the two-dimensional case. Asymptotic upper…
The weighted star discrepancy of point sets appears in the weighted Koksma-Hlawka inequality and thus is a measure for the quality of point sets with respect to their performance in quasi-Monte Carlo algorithms. A special choice of point…
Deterministically generating near-uniform point samplings of the motion groups like SO(3), SE(3) and their n-wise products SO(3)^n, SE(3)^n is fundamental to numerous applications in computational and data sciences. The natural measure of…
Inconsistent values are commonly encountered in real-world applications, which can negatively impact data analysis and decision-making. While existing research primarily focuses on identifying the smallest removal set to resolve…
The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
With the aim of generalizing histogram statistics to higher dimensional cases, density estimation via discrepancy based sequential partition (DSP) has been proposed to learn an adaptive piecewise constant approximation defined on a binary…
In the present paper we prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure $\mu$ on the $d$-dimensional unit cube. We improve a theorem of Beck, by showing that for…
Cut and project sets are obtained by taking an irrational slice of a lattice and projecting it to a lower dimensional subspace, and are fully characterised by the shape of the slice (window) and the choice of the lattice. In this context we…
Diffractive lenses have recently been applied to the domain of multispectral imaging in the X-ray and UV regimes where they can achieve very high resolution as compared to reflective and refractive optics. Conventionally, spectral…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
We discuss the problem of defining an estimate for the error in quasi-Monte Carlo integration. The key issue is the definition of an ensemble of quasi-random point sets that, on the one hand, includes a sufficiency of equivalent point sets,…
Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
Given a set of points in the plane, the \textsc{General Position Subset Selection} problem is that of finding a maximum-size subset of points in general position, i.e., with no three points collinear. The problem is known to be ${\rm…