Objective and efficient inference for couplings in neuronal network*This article is an updated version of: Terada Y, Obuchi T, Isomura T and Kabashima Y 2018 Objective and efficient inference for couplings in neuronal networks Advances in Neural Information Processing Systems 31 ed S Bengio, H Wallach, H Larochelle, K Grauman, N Cesa-Bianchi and R Garnett (Red Hook, NY: Curran Associates, Inc) pp 4971–4980. (20th December 2019)