Intrinsic limitations of inverse inference in the pairwise Ising spin glass

Abstract

We analyze the limits inherent to the inverse reconstruction of a pairwise Ising spin glass based on susceptibility propagation. We establish the conditions under which the susceptibility propagation algorithm is able to reconstruct the characteristics of the network given first- and second-order local observables, evaluate eventual errors due to various types of noise in the originally observed data, and discuss the scaling of the problem with the number of degrees of freedom.

References in corpus (4)

• Identification of direct residue contacts in protein-protein interaction by message passing
• The Ising Model for Neural Data: Model Quality and Approximate Methods for Extracting Functional Connectivity
• Statistical physics of pairwise probability models
• Small-correlation expansions for the inverse Ising problem

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• Susceptibility Propagation by Using Diagonal Consistency
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• Counting solutions from finite samplings
• Beyond inverse Ising model: structure of the analytical solution for a class of inverse problems
• Message passing algorithms for the Hopfield network reconstruction: threshold behavior and limitation
• State sampling dependence of the Hopfield network inference
• Solving Non-parametric Inverse Problem in Continuous Markov Random Field using Loopy Belief Propagation