# Estimating Time-Varying Graphical Models

arXiv: https://arxiv.org/abs/1804.03811 · HTML: https://mlsanity.com/paper/1804.03811/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2018.

## Built on by (most cited first, 8 of 8)

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [High-Dimensional Differential Parameter Inference in Exponential Family using Time Score Matching](https://mlsanity.com/paper/2410.10637/) (2024)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [The non-overlapping statistical approximation to overlapping group lasso](https://mlsanity.com/paper/2211.09221/) (2022)
- [Nonparametric learning of heterogeneous graphical model on network-linked data](https://mlsanity.com/paper/2507.01473/) (2025)
- [Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso](https://mlsanity.com/paper/2602.08197/) (2026)
- [TVGL-CFM:Generating and Forecasting Time-Varying Trajectories of Dynamic Networks with Conditional Flow Matching](https://mlsanity.com/paper/2607.16894/) (2026)

## Abstract (arXiv)

In this paper, we study time-varying graphical models based on data measured over a temporal grid. Such models are motivated by the needs to describe and understand evolving interacting relationships among a set of random variables in many real applications, for instance the study of how stocks interact with each other and how such interactions change over time. We propose a new model, LOcal Group Graphical Lasso Estimation (loggle), under the assumption that the graph topology changes gradually over time. Specifically, loggle uses a novel local group-lasso type penalty to efficiently incorporate information from neighboring time points and to impose structural smoothness of the graphs. We implement an ADMM based algorithm to fit the loggle model. This algorithm utilizes blockwise fast computation and pseudo-likelihood approximation to improve computational efficiency. An R package loggle has also been developed. We evaluate the performance of loggle by simulation experiments. We also apply loggle to S&P 500 stock price data and demonstrate that loggle is able to reveal the interacting relationships among stocks and among industrial sectors in a time period that covers the recent global financial crisis.