EAGER: Learning Graphical Models of High-Dimensional Time Series

Undirected graphical models have been increasingly used for exploring or exploiting dependency structures among different random variables underlying multivariate data, representing complex systems. Graphical models are an important and useful tool for analyzing multivariate data. A graphical model is a statistical model where random variables and the conditional dependencies between them are specified via a graph. Graphical models were originally developed for random vectors with multiple independent realizations (independent and identically distributed time series). Such models have been extensively studied, and found to be useful in a wide variety of applications such as biological regulatory networks, functional brain networks, and social networks. They have also proved to be useful for clustering, semi-supervised learning and classification tasks. Graphical modeling of time-dependent data (time series) is more recent. Time series graphical models of dependent data have been applied to intensive care monitoring, financial time series, air pollution data, and analysis of functional magnetic resonance imaging data to provide insights into the functional connectivity of different brain regions. Almost all existing works on dependent time series are limited to low-dimensional series where number of variables is much smaller than the data sample size. To address high-dimensional time series where number of variables exceed, or are comparable to, the sample size, it is (almost always) assumed that the series is independent and identically distributed in choice of objective function, and algorithm design and analysis, for both synthetic and real data. This project aims to fill this gap by focusing on methods for graphical modeling of high-dimensional dependent time series. The project will also provide training and research experiences for graduate students.

Novel, innovative, general statistical signal processing approaches to graphical modeling of real-valued dependent multivariate time series in high-dimensional settings are investigated in this research. An emphasis is on frequency-domain approaches without requiring detailed parametric modeling of the underlying time series to capture any dependencies in the time domain. Frequency-domain formulation leads to consideration of complex-valued Gaussian graphical models for proper Gaussian random vectors, a topic that has received scant attention. The following thrusts form the core of this research: (1) Design, analysis and optimization of penalized log-likelihood functions to fit graphical models. (2) Analysis of theoretical properties (such as consistency and sparsistency) of the obtained solutions. (3) Application to synthetic and real data to evaluate the efficacy and computational efficiency of the considered approaches.

J.K. Tugnait, "Estimation of differential graphs via log-sum penalized D-trace loss" in Proc. 22nd IEEE Statistical Signal Processing Workshop (SSP-2023), pp. 240-244, Hanoi, Vietnam, July 2-5, 2023.

J.K. Tugnait, "Sparse high-dimensional matrix-valued graphical model learning from dependent data," in Proc. 22nd IEEE Statistical Signal Processing Workshop (SSP-2023), pp. 344-348, Hanoi, Vietnam, July 2-5, 2023.

J.K. Tugnait, "Estimation of high-dimensional differential graphs from multi-attribute data," in Proc. 2023 IEEE Intern. Conf. Acoustics, Speech & Signal Processing (ICASSP 2023), Rhodes Island, Greece, June 5-9, 2023.

J.K. Tugnait, "On graphical modeling of high-dimensional long-range dependent time series" in Proc. 56th Asilomar Conference on Signals, Systems and Computers (ASILOMAR 2022), pp. 1098-1102, Pacific Grove, CA, Oct. 30 - Nov. 2, 2022

J.K. Tugnait, "Graph learning from multivariate dependent time series via a multi-attribute formulation" in Proc. 2022 IEEE Intern. Conf. Acoustics, Speech & Signal Processing (ICASSP 2022), pp. 4508-4512, Singapore, May 22-27, 2022. [pdf]

J.K. Tugnait, "Sparse-group log-sum penalized graphical model learning for time series," in Proc. 2022 IEEE Intern. Conf. Acoustics, Speech & Signal Processing (ICASSP 2022), pp. 5822-5826, Singapore, May 22-27, 2022. [pdf]

J.K. Tugnait, "On sparse high-dimensional graphical model learning for dependent time series," Signal Processing, vol. 197, Aug. 2022, Article 108539. [pdf:arXiv] [pdf:journal]

J.K. Tugnait, "On sparse graph estimation under statistical and Laplacian constraints," in Proc. 13th Asia Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC 2021), pp. 232-239, Tokyo, Japan, Dec. 14-17, 2021.

J.K. Tugnait, "On high-dimensional graph learning under total positivity," in Proc. 55th Asilomar Conference on Signals, Systems and Computers, pp. 1274-1278, Pacific Grove, CA, Oct. 31 -- Nov 3, 2021.

J.K. Tugnait, "New results on graphical modeling of high-dimensional dependent time series," in Proc. 55th Asilomar Conference on Signals, Systems and Computers, pp. 162-166, Pacific Grove, CA, Oct. 31 -- Nov 3, 2021.

J.K. Tugnait, "Sparse graph learning under Laplacian-related constraints," IEEE Access, vol. 9, pp. 151067-151079, 2021. [pdf]

J.K. Tugnait, "Corrections to 'Sparse-group lasso for graph learning from multi-attribute data'," IEEE Trans. Signal Processing, vol. 69, p. 4758, 2021. [pdf]

J.K. Tugnait, "Sparse-group lasso for graph learning from multi-attribute data," IEEE Trans. Signal Processing, vol. 69, pp. 1771-1786, 2021. [pdf]

J.K. Tugnait, "Consistency of sparse-group lasso graphical model selection for time series," in Proc. 54th Asilomar Conference on Signals, Systems and Computers, pp. 589-593, Pacific Grove, CA, Nov. 1-4, 2020.

J.K. Tugnait, "Deviance tests for graph estimation from multi-attribute Gaussian data," IEEE Trans. Signal Processing, vol. 68, pp. 5632-5647, 2020. [pdf]

J.K. Tugnait, "Graph learning from multi-attribute smooth signals," in Proc. 2020 IEEE Intern. Workshop on Machine Learning for Signal Processing (MLSP 2020), Espoo, Finland, Sept. 21-24, 2020.

J.K. Tugnait, "SCAD-penalized complex Gaussian graphical model selection," in Proc. 2020 IEEE Intern. Workshop on Machine Learning for Signal Processing (MLSP 2020), Espoo, Finland, Sept. 21-24, 2020.

Date of latest revision: tue oct 10 2023