Gauging variational inference*This article is an updated version of: Ahn S, Chertkov M and Shin J 2017 Gauging variational inference Advances in Neural Information Processing Systems 30 ed I Guyon, U V Luxburg, S Bengio, H Wallach, R Fergus, S Vishwanathan and R Garnett (Red Hook, NY: Curran Associates, Inc.) pp 2881–2890. (20th December 2019)