6 papers
A Bayesian Approach to Low-Discrepancy Subset Selection
Nathan Kirk
Low-discrepancy designs play a central role in quasi-Monte Carlo methods and are increasingly influential in other domains such as machine learning, robotics and computer graphics,…
Multilevel Sampling in Algebraic Statistics
Nathan Kirk, Ivan GvozdanoviÄ, Sonja PetroviÄ
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)…
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…
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…