Enhancing Markov Chain Monte Carlo Sampling Methods with Deep Learning

Explore advanced techniques for enhancing Markov Chain Monte Carlo (MCMC) sampling methods using deep learning in this 46-minute lecture by Eric Vanden-Eijnden. Delve into key concepts including probabilities, expectations, and Monte-Carlo sampling before examining the intersection of sampling and learning. Investigate importance sampling, transport, and the application of normalizing flows to assist MCMC sampling. Learn about MCMC with normalizing flows for sampling random fields and Bayesian inference. Discover the Non-Equilibrium Importance Sampling (NEIS) technique and its applications to Gaussian mixtures and Neal's Funnel Distribution. Gain valuable insights into cutting-edge approaches for improving sampling methods in high-dimensional spaces.

Intro
Probabilities and Expectations
Monte-Carlo Sampling
Sampling and Learning
Outline
Importance Sampling and Transport
Assisting MCMC Sampling with Normalizing Flows
MCMC with NF for Sampling of Random Fields
MCMC with NF for Bayesian Inference
Non-Equilibrium Importance Sampling (NEIS)
NEIS for Gaussian Mixtures in 5D & 10D
NEIS for Neal's Funnel Distribution in 100
Concluding remarks