Intrinsic limitations of inverse inference in the pairwise Ising spin glass

TL;DR

This paper investigates the fundamental limitations of using susceptibility propagation for inverse inference in pairwise Ising spin glasses, focusing on reconstruction accuracy, noise effects, and scalability.

Contribution

It establishes the conditions for successful network reconstruction and analyzes the impact of noise and system size on the inverse inference process.

Findings

Susceptibility propagation can reconstruct network features under specific conditions.

Noise in data causes errors in the inverse inference process.

The complexity of the problem scales with the number of degrees of freedom.

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.