Computational Math and Statistics Seminar by Nathan Kirk: What Can Machine Learning do for Quasi-Monte Carlo Methods (and visa versa)?

Speaker: Nathan Kirk, senior research associate, Illinois Institute of Technology 

Title: What Can Machine Learning do for Quasi-Monte Carlo Methods (and visa versa)?

Abstract:

This talk presents the first machine-learning method for the generation of low-discrepancy (highly uniform) point sets in the hypercube, dubbed Message-Passing Monte Carlo sets. We leverage tools from geometric deep learning and base our model on graph neural networks. We further provide an extension of our framework to higher dimensions, which flexibly allows the generation of custom-made points that emphasize the uniformity in specific dimensions that are primarily important for the particular problem at hand. We demonstrate that our proposed model achieves state-of-the-art performance superior to previous methods by a significant margin. Finally, I hope to also present early work employing low-discrepancy point sets to improve Neural Autoregressive Distribution Estimators in the context of image generation.

Computational Mathematics and Statistics Seminar