Generalized belief propagation for estimating the partition function of the 2D Ising model
Chun Lam Chan, Mahdi Jafari Siavoshani, Sidharth Jaggi, Navin Kashyap, Pascal O. Vontobel · 2015
Recent empirical results have demonstrated that generalized belief propagation (GBP) can be used to closely estimate the capacity of certain 2D runlength-limited constraints. We provide a partial analytical validation of these observations by showing that GBP yields a lower bound on the partition function of 2D Ising models with restricted grid size. While previous papers have proved that belief propagation (BP) can be used to obtain a lower bound on the partition function of 2D Ising models, this paper is the first work that analyzes GBP-based partition function approximations of 2D Ising models.