Explore a 44-minute lecture on approximating the total variation (TV) distance between two product distributions. Delve into the fundamental metric used to measure differences between distributions, as presented by Weiming Feng from the University of Edinburgh. Learn about the recent developments in this field, including the #P-hardness of exact TV distance computation for product distributions over the Boolean domain. Discover two approximation algorithms: a randomized approach utilizing coupling techniques and a deterministic method based on distribution sparsification. Gain insights into the challenges and progress made in this area of probabilistic circuits and logic research.