# Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation

arXiv: https://arxiv.org/abs/2205.00007 · HTML: https://mlsanity.com/paper/2205.00007/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 21 references that are in the map.
- First posted on arXiv 29 Apr 2022.

## Builds on (most cited first, 4 of 4)

- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [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)
- [Estimation of Large Covariance and Precision Matrices from Temporally Dependent Observations](https://mlsanity.com/paper/1412.5059/) (2014)

## Built on by (most cited first, 1 of 1)

- [On Conditional Independence Graph Learning From Multi-Attribute Gaussian Dependent Time Series](https://mlsanity.com/paper/2512.07557/) (2025)

## Abstract (arXiv)

We consider the problem of inferring the conditional independence graph (CIG) of a high-dimensional stationary multivariate Gaussian time series. In a time series graph, each component of the vector series is represented by distinct node, and associations between components are represented by edges between the corresponding nodes. We formulate the problem as one of multi-attribute graph estimation for random vectors where a vector is associated with each node of the graph. At each node, the associated random vector consists of a time series component and its delayed copies. We present an alternating direction method of multipliers (ADMM) solution to minimize a sparse-group lasso penalized negative pseudo log-likelihood objective function to estimate the precision matrix of the random vector associated with the entire multi-attribute graph. The time series CIG is then inferred from the estimated precision matrix. A theoretical analysis is provided. Numerical results illustrate the proposed approach which outperforms existing frequency-domain approaches in correctly detecting the graph edges.