# Time-dependent spatially varying graphical models, with application to brain fMRI data analysis

arXiv: https://arxiv.org/abs/1711.03701 · HTML: https://mlsanity.com/paper/1711.03701/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Nov 2017.

## Built on by (most cited first, 7 of 7)

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Scalable Inference of Sparsely-changing Markov Random Fields with Strong Statistical Guarantees](https://mlsanity.com/paper/2102.03585/) (2021)
- [Efficient Inference of Spatially-varying Gaussian Markov Random Fields with Applications in Gene Regulatory Networks](https://mlsanity.com/paper/2206.10174/) (2022)
- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)
- [Enhancing Graphical Lasso: A Robust Scheme for Non-Stationary Mean Data](https://mlsanity.com/paper/2503.19651/) (2025)
- [Interpretable Dynamic Network Modeling of Tensor Time Series via Kronecker Time-Varying Graphical Lasso](https://mlsanity.com/paper/2602.08197/) (2026)
- [Transfer Learning in High-dimensional Ising Models](https://mlsanity.com/paper/2607.03005/) (2026)

## Abstract (arXiv)

In this work, we present an additive model for space-time data that splits the data into a temporally correlated component and a spatially correlated component. We model the spatially correlated portion using a time-varying Gaussian graphical model. Under assumptions on the smoothness of changes in covariance matrices, we derive strong single sample convergence results, confirming our ability to estimate meaningful graphical structures as they evolve over time. We apply our methodology to the discovery of time-varying spatial structures in human brain fMRI signals.