Learning the piece-wise constant graph structure of a varying Ising model
This work addresses the challenge of detecting unknown numbers of change-points in time-varying Ising models, which is incremental as it builds on existing graph estimation methods by incorporating change-point detection.
The paper tackles the problem of estimating multiple change-points and underlying graph structures in a time-varying Ising model that evolves piece-wise constantly, proposing a penalized conditional log-likelihood method that achieves sparsity and piece-wise constant evolution, with experimental results demonstrating its performance on synthetic and real-world datasets.
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.