# Joint Estimation of Multiple Graphical Models from High Dimensional Time Series

arXiv: https://arxiv.org/abs/1311.0219 · HTML: https://mlsanity.com/paper/1311.0219/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2013.

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

- [Joint Gaussian Graphical Model Estimation: A Survey](https://mlsanity.com/paper/2110.10281/) (2021)
- [Testing Directed Acyclic Graph via Structural, Supervised and Generative Adversarial Learning](https://mlsanity.com/paper/2106.01474/) (2021)
- [Latent Multimodal Functional Graphical Model Estimation](https://mlsanity.com/paper/2210.17237/) (2022)
- [Joint Estimation and Inference for Multi-Experiment Networks of High-Dimensional Point Processes](https://mlsanity.com/paper/2109.11634/) (2021)
- [Solution Path of Time-varying Markov Random Fields with Discrete Regularization](https://mlsanity.com/paper/2307.13750/) (2023)
- [A spectral clustering-type algorithm for the consistent estimation of the Hurst distribution in moderately high dimensions](https://mlsanity.com/paper/2501.18115/) (2025)
- [High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series](https://mlsanity.com/paper/2609.30565/) (2026)

## Abstract (arXiv)

In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical models of subjects vary, but are assumed to change smoothly corresponding to a measure of closeness between subjects. We propose a kernel based method for jointly estimating all graphical models. Theoretically, under a double asymptotic framework, where both (T,n) and the dimension d can increase, we provide the explicit rate of convergence in parameter estimation. It characterizes the strength one can borrow across different individuals and impact of data dependence on parameter estimation. Empirically, experiments on both synthetic and real resting state functional magnetic resonance imaging (rs-fMRI) data illustrate the effectiveness of the proposed method.