On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series

Autor:	Tugnait, Jitendra K.
Rok vydání:	2021
Předmět:	Electrical Engineering and Systems Science - Signal Processing Computer Science - Machine Learning Statistics - Machine Learning
Zdroj:	Signal Processing, vol. 197, pp. 1-18, Aug. 2022, Article 108539
Druh dokumentu:	Working Paper
DOI:	10.1016/j.sigpro.2022.108539
Popis:	We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso-based frequency-domain formulation of the problem based on frequency-domain sufficient statistic for the observed time series is presented. We investigate an alternating direction method of multipliers (ADMM) approach for optimization of the sparse-group lasso penalized log-likelihood. We provide sufficient conditions for convergence in the Frobenius norm of the inverse PSD estimators to the true value, jointly across all frequencies, where the number of frequencies are allowed to increase with sample size. This results also yields a rate of convergence. We also empirically investigate selection of the tuning parameters based on Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data. Comment: 20 pages, 5 figures. Published in Signal Processing. Latest version (June 4, 2024) corrects some typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.07897 Zobrazit plný text záznamu View this record from Arxiv