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

arXiv: https://arxiv.org/abs/2111.07897 · HTML: https://mlsanity.com/paper/2111.07897/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 66 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 10 of 10)

- [A Unified Framework for Sparse Relaxed Regularized Regression: SR3](https://mlsanity.com/paper/1807.05411/) (2018)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees](https://mlsanity.com/paper/1307.5381/) (2013)
- [Bayesian Structure Learning for Stationary Time Series](https://mlsanity.com/paper/1505.03131/) (2015)
- [Compound Rank-k Projections for Bilinear Analysis](https://mlsanity.com/paper/1411.6231/) (2014)
- [Learning the Conditional Independence Structure of Stationary Time Series: A Multitask Learning Approach](https://mlsanity.com/paper/1404.1361/) (2014)
- [On the Sample Complexity of Graphical Model Selection for Non-Stationary Processes](https://mlsanity.com/paper/1701.04724/) (2017)
- [Compressive Nonparametric Graphical Model Selection For Time Series](https://mlsanity.com/paper/1311.3257/) (2013)
- [Direction of arrival estimation using robust complex Lasso](https://mlsanity.com/paper/1605.03824/) (2016)

## Built on by (most cited first, 6 of 6)

- [Learning Sparse High-Dimensional Matrix-Valued Graphical Models From Dependent Data](https://mlsanity.com/paper/2404.19073/) (2024)
- [Learning Multi-Frequency Partial Correlation Graphs](https://mlsanity.com/paper/2311.15756/) (2023)
- [Learning Conditional Independence Differential Graphs From Time-Dependent Data](https://mlsanity.com/paper/2512.06960/) (2025)
- [On Conditional Independence Graph Learning From Multi-Attribute Gaussian Dependent Time Series](https://mlsanity.com/paper/2512.07557/) (2025)
- [Time Series Gaussian Chain Graph Models](https://mlsanity.com/paper/2604.07018/) (2026)
- [Inference for High-Dimensional Sparse Spectral Precision Matrices](https://mlsanity.com/paper/2606.07986/) (2026)

## Abstract (arXiv)

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.