5 papers
Optimizing Kernel Discrepancies via Subset Selection
Deyao Chen, François Clément, Carola Doerr +1
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…
High-Dimensional Quasi-Monte Carlo via Combinatorial Discrepancy
Jiaheng Chen, Haotian Jiang, Nathan Kirk
Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods are classical approaches for the numerical integration of functions over . While QMC methods can achieve faster co…
Enhancing Neural Autoregressive Distribution Estimators for Image Reconstruction
Ambrose Emmett-Iwaniw, Nathan Kirk
Autoregressive models are often employed to learn distributions of image data by decomposing the -dimensional density function into a product of one-dimensional conditional dist…
Multilevel Sampling in Algebraic Statistics
Nathan Kirk, Ivan Gvozdanović, Sonja Petrović
This paper proposes a multilevel sampling algorithm for fiber sampling problems in algebraic statistics, inspired by Henry Wynn's suggestion to adapt multilevel Monte Carlo (MLMC)…
Quasi-Monte Carlo Methods: What, Why, and How?
Fred J. Hickernell, Nathan Kirk, Aleksei G. Sorokin
Many questions in quantitative finance, uncertainty quantification, and other disciplines are answered by computing the population mean, , where instances of $Y:…