is to be found and Hopfield-like models [@Hopfield; @CoMoSe] are likely to be more relevant. To be mentioned also is a recent mean-field methods [@NgBe2] which allows one to find in some simple cases the Ising couplings of a low temperature model, i.e. displaying multiple probabilistic modes.

On the side of inverse Gaussian problem, not surprisingly similar methods have been developed by explicitly performing $L_0$ and $L_1$ matrix norm penalizations on the inverse covariance matrices, so as to determine sparse non-zero couplings in estimated inverse covariance matrices for large-scale statistical inference applications [@FrHaTi; @HSDR] where direct inversion is not amenable. In our context the goal is a bit different. In general cases, the underlying inverse covariance matrix is not necessarily sparse. What we aim to find is a good sparse approximation to the exact inverse covariance matrix. Furthermore, sparsity constraint is not enough for constructing graph structure to be used in conjunction with BP. Known sufficient conditions celled walk-summability [@MaJoWi] (WS) are likely to be imposed instead of (or in addition to) the sparsity constraint. To the best of our knowledge not much work is taking this point into consideration at the noticeable exception of [@AnTaHuWi] by restricting the class 