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

Batiste Le Bars, Pierre Humbert, Argyris Kalogeratos, Nicolas Vayatis
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:675-684, 2020.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-bars20a, title = {Learning the piece-wise constant graph structure of a varying Ising model}, author = {Bars, Batiste Le and Humbert, Pierre and Kalogeratos, Argyris and Vayatis, Nicolas}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {675--684}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/bars20a/bars20a.pdf}, url = {https://proceedings.mlr.press/v119/bars20a.html}, 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.} }
Endnote
%0 Conference Paper %T Learning the piece-wise constant graph structure of a varying Ising model %A Batiste Le Bars %A Pierre Humbert %A Argyris Kalogeratos %A Nicolas Vayatis %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-bars20a %I PMLR %P 675--684 %U https://proceedings.mlr.press/v119/bars20a.html %V 119 %X 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.
APA
Bars, B.L., Humbert, P., Kalogeratos, A. & Vayatis, N.. (2020). Learning the piece-wise constant graph structure of a varying Ising model. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:675-684 Available from https://proceedings.mlr.press/v119/bars20a.html.

Related Material