Learning the piece-wise constant graph structure of a varying Ising model

TL;DR

This paper introduces a method for detecting change-points and learning the evolving graph structure in a piece-wise constant, time-varying Ising model, combining penalized likelihood estimation with theoretical guarantees.

Contribution

It proposes a novel approach for simultaneous change-point detection and graph structure learning in time-varying Ising models with proven consistency results.

Findings

Effective detection of change-points in synthetic datasets

Accurate graph structure estimation in real-world data

Theoretical guarantees for change-point consistency

Abstract

This work focuses on the estimation of multiple change-points in a time-varying Ising model that evolves piece-wise constantly. The aim is to identify both the moments at which significant changes occur in the Ising model, as well as the underlying graph structures. For this purpose, we propose to estimate the neighborhood of each node by maximizing a penalized version of its conditional log-likelihood. The objective of the penalization is twofold: it imposes sparsity in the learned graphs and, thanks to a fused-type penalty, it also enforces them to evolve piece-wise constantly. Using few assumptions, we provide two change-points consistency theorems. Those are the first in the context of unknown number of change-points detection in time-varying Ising model. Finally, experimental results on several synthetic datasets and a real-world dataset demonstrate the performance of our method.