Computing marginals of probability distributions (magnetizations, spin-spin correlations etc) is an important problem in statistical physics of disordered systems and many other fields. In applications to decision and inference problems one typically wants to estimate the likelihood that a single variable takes a given value, given the interactions with all the other variables, and then decide that this variable takes its most likely value or estimate the most likely configuration of all the variables.
Over the last decade there has therefore been intense interest in a class of "message-passing" methods to approximate compute marginals of Boltzmann-Gibbs distributions (the cavity method, Belief Propagation, iterative decoding), for which the canonical reference is the recent monograph by M Mezard and A Montanari [1].
In this talk I will describe in some detail work with Hamed Mahmoudi [2-4] to extend such methods to describe stationary states of some simple non-equilibrium systems (kinetic Ising models with asymmetric interactions). Except for special cases message-passing here does not work without additional assumptions, but can still outperform the well-known "dynamic mean-field" and more recently developed "dynamic TAP" approximations.
[1] M Mezard & A Montanari "Information, Physics, and Computation", Oxford University Press (2009)
[2] E Aurell & H Mahmoudi, JSTAT (2011) P04014
[3] E Aurell & H Mahmoudi, Communications in Theoretical Physics (2011) pp. 157-162
[4] E Aurell & H Mahmoudi, "Dynamic mean-field and dynamic cavity for diluted Ising systems", arXiv:1109.3399
