Underdamped Langevin Monte Carlo

Underdamped Langevin Monte Carlo (ULMC) is a sampling technique used to efficiently draw samples from complex, high-dimensional probability distributions, particularly those arising in Bayesian inference and machine learning. Current research focuses on improving ULMC's scalability and accuracy, particularly for constrained sampling problems and non-convex target distributions, with algorithms incorporating penalty methods and stochastic gradient updates showing promise. These advancements are significant because efficient sampling from complex distributions is crucial for solving inverse problems, accelerating Bayesian inference, and enabling the training of sophisticated models in various fields.