A fast and accurate algorithm for inferring sparse Ising models via parameters activation to maximize the pseudo-likelihood

TL;DR

This paper introduces PAMPL, a fast and accurate algorithm for inferring sparse Ising models by optimizing parameters to maximize pseudo-likelihood, outperforming existing methods in various network topologies.

Contribution

The paper presents PAMPL, a novel algorithm that enhances pseudo-likelihood based inference for sparse Ising models through a targeted parameter activation strategy.

Findings

PAMPL outperforms existing algorithms in speed and accuracy.

Effective on various graph structures including random graphs and lattices.

Works well with both ferromagnetic and spin glass couplings.

Abstract

We propose a new algorithm to learn the network of the interactions of pairwise Ising models. The algorithm is based on the pseudo-likelihood method (PLM), that has already been proven to efficiently solve the problem in a large variety of cases. Our present implementation is particularly suitable to address the case of sparse underlying topologies and it is based on a careful search of the most important parameters in their high dimensional space. We call this algorithm Parameters Activation to Maximize Pseudo-Likelihood (PAMPL). Numerical tests have been performed on a wide class of models such as random graphs and finite dimensional lattices with different type of couplings, both ferromagnetic and spin glasses. These tests show that PAMPL improves the performances of the fastest existing algorithms.