Calculation of Discrepancy Measures and Applications

Abstract

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 discrepancy measures in a more general context, we focus on the geometric discrepancy measures for which computation algorithms have been designed. In particular, we explain methods to determine $L_2$-discrepancies and approaches to tackle the inherently difficult problem to calculate the star discrepancy of given sample sets. We also discuss in more detail three applications of algorithms to approximate discrepancies.

References in corpus (1)

• Constructing Low Star Discrepancy Point Sets with Genetic Algorithms

Cited by in corpus (17)

• Constructing Low Star Discrepancy Point Sets with Genetic Algorithms
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• On Quasi-Isometry of Threshold-Based Sampling
• Density Estimation via Discrepancy Based Adaptive Sequential Partition
• A Generalized Faulhaber Inequality, Improved Bracketing Covers, and Applications to Discrepancy
• Message-Passing Monte Carlo: Generating low-discrepancy point sets via Graph Neural Networks
• Computing Star Discrepancies with Numerical Black-Box Optimization Algorithms
• Density Estimation via Discrepancy
• Discovering and Visualizing Hierarchy in Multivariate Data
• Some Results on the Complexity of Numerical Integration
• Extremal Distributions of Discrepancy functions
• Quasi Monte Carlo inverse transform sampling for phase space conserving Lagrangian particle methods and Eulerian-Lagrangian coupling
• Computable error bounds for quasi-Monte Carlo using points with non-negative local discrepancy
• New Bounds for the Extreme and the Star Discrepancy of Double-Infinite Matrices
• Local Extrema in Quantum Chaos
• On the Discrepancy Normed Space of Event Sequences for Threshold-based Sampling
• On the Discrepancy of Jittered Sampling