# On Conditional Independence Graph Learning From Multi-Attribute Gaussian Dependent Time Series

arXiv: https://arxiv.org/abs/2512.07557 · HTML: https://mlsanity.com/paper/2512.07557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 55 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 8 of 8)

- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Support recovery without incoherence: A case for nonconvex regularization](https://mlsanity.com/paper/1412.5632/) (2014)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [FuDGE: A Method to Estimate a Functional Differential Graph in a High-Dimensional Setting](https://mlsanity.com/paper/2003.05402/) (2020)
- [On Sparse High-Dimensional Graphical Model Learning For Dependent Time Series](https://mlsanity.com/paper/2111.07897/) (2021)
- [Identification of Sparse Reciprocal Graphical Models](https://mlsanity.com/paper/1806.04423/) (2018)
- [Sparse-Group Log-Sum Penalized Graphical Model Learning For Time Series](https://mlsanity.com/paper/2204.13824/) (2022)
- [Graph Learning from Multivariate Dependent Time Series via a Multi-Attribute Formulation](https://mlsanity.com/paper/2205.00007/) (2022)

## Abstract (arXiv)

Estimation of the conditional independence graph (CIG) of high-dimensional multivariate Gaussian time series from multi-attribute data is considered. Existing methods for graph estimation for such data are based on single-attribute models where one associates a scalar time series with each node. In multi-attribute graphical models, each node represents a random vector or vector time series. In this paper we provide a unified theoretical analysis of multi-attribute graph learning for dependent time series using a penalized log-likelihood objective function formulated in the frequency domain using the discrete Fourier transform of the time-domain data. We consider both convex (sparse-group lasso) and non-convex (log-sum and SCAD group penalties) penalty/regularization functions. We establish sufficient conditions in a high-dimensional setting for consistency (convergence of the inverse power spectral density to true value in the Frobenius norm), local convexity when using non-convex penalties, and graph recovery. We do not impose any incoherence or irrepresentability condition for our convergence results. We also empirically investigate selection of the tuning parameters based on the Bayesian information criterion, and illustrate our approach using numerical examples utilizing both synthetic and real data.