Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series
Abstract
We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. A sparse-group lasso based frequency-domain formulation of the problem has been considered in the literature where the objective is to estimate the sparse inverse power spectral density (PSD) of the data. The CIG is then inferred from the estimated inverse PSD. In this paper we investigate use of a sparse-group log-sum penalty (LSP) instead of sparse-group lasso penalty. An alternating direction method of multipliers (ADMM) approach for iterative optimization of the non-convex problem is presented. We provide sufficient conditions for local convergence in the Frobenius norm of the inverse PSD estimators to the true value. This results also yields a rate of convergence. We illustrate our approach using numerical examples utilizing both synthetic and real data.
Cite
@article{arxiv.2204.13824,
title = {Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series},
author = {Jitendra K Tugnait},
journal= {arXiv preprint arXiv:2204.13824},
year = {2022}
}
Comments
5 pages, 2 figures, accepted to 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2022), Singapore, May 22-27, 2022. Some typos in the conference version have been corrected. arXiv admin note: substantial text overlap with arXiv:2111.07897