Pseudolikelihood Decimation Algorithm Improving the Inference of the Interaction Network in a General Class of Ising Models

TL;DR

This paper introduces a fully automated decimation algorithm based on pseudolikelihood maximization that improves the inference of interaction networks in Ising models across various topologies and coupling types.

Contribution

The authors develop a novel decimation procedure that enhances the accuracy of network inference in Ising models without subjective parameter choices.

Findings

The new algorithm outperforms standard pseudolikelihood methods.

It effectively distinguishes relevant couplings across different temperatures.

The method is applicable to diverse Ising model topologies.

Abstract

In this Letter we propose a new method to infer the topology of the interaction network in pairwise models with Ising variables. By using the pseudolikelihood method (PLM) at high temperature, it is generally possible to distinguish between zero and nonzero couplings because a clear gap separate the two groups. However at lower temperatures the PLM is much less effective and the result depends on subjective choices, such as the value of the $\ell_1$ regularizer and that of the threshold to separate nonzero couplings from null ones. We introduce a decimation procedure based on the PLM that recursively sets to zero the less significant couplings, until the variation of the pseudolikelihood signals that relevant couplings are being removed. The new method is fully automated and does not require any subjective choice by the user. Numerical tests have been performed on a wide class of Ising models, having different topologies (from random graphs to finite dimensional lattices) and different couplings (both diluted ferromagnets in a field and spin glasses). These numerical results show that the new algorithm performs better than standard PLM