1112.3501 (H. Chau Nguyen et al.)

Bethe-Peierls approximation and the inverse Ising model    [PDF]

H. Chau Nguyen, Johannes Berg

We apply the Bethe-Peierls approximation to the problem of the inverse Ising
model and show how the linear response relation leads to a simple method to
reconstruct couplings and fields of the Ising model. This reconstruction is
exact on tree graphs, yet its computational expense is comparable to other
mean-field methods. We compare the performance of this method to the
independent-pair, naive mean- field, Thouless-Anderson-Palmer approximations,
the Sessak-Monasson expansion, and susceptibility propagation in the Cayley
tree, SK-model and random graph with fixed connectivity. At low temperatures,
Bethe reconstruction outperforms all these methods, while at high temperatures
it is comparable to the best method available so far (Sessak-Monasson). The
relationship between Bethe reconstruction and other mean- field methods is
discussed.

View original: http://arxiv.org/abs/1112.3501