# Distributed Estimation of Sparse Inverse Covariances

arXiv: https://arxiv.org/abs/2109.12020 · HTML: https://mlsanity.com/paper/2109.12020/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 7 of 7)

- [Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data](https://mlsanity.com/paper/1706.03161/) (2017)
- [Node-Based Learning of Multiple Gaussian Graphical Models](https://mlsanity.com/paper/1303.5145/) (2013)
- [Learning Graphs with Monotone Topology Properties and Multiple Connected Components](https://mlsanity.com/paper/1705.10934/) (2017)
- [Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation](https://mlsanity.com/paper/1306.3212/) (2013)
- [G-AMA: Sparse Gaussian graphical model estimation via alternating minimization](https://mlsanity.com/paper/1405.3034/) (2014)
- [Network-Scale Traffic Modeling and Forecasting with Graphical Lasso and Neural Networks](https://mlsanity.com/paper/1801.00711/) (2017)
- [Graphic-theoretic distributed inference in social networks](https://mlsanity.com/paper/1402.0918/) (2014)

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

- [Robust Online and Distributed Mean Estimation Under Adversarial Data Corruption](https://mlsanity.com/paper/2209.09624/) (2022)

## Abstract (arXiv)

Learning the relationships between various entities from time-series data is essential in many applications. Gaussian graphical models have been studied to infer these relationships. However, existing algorithms process data in a batch at a central location, limiting their applications in scenarios where data is gathered by different agents. In this paper, we propose a distributed sparse inverse covariance algorithm to learn the network structure (i.e., dependencies among observed entities) in real-time from data collected by distributed agents. Our approach is built on an online graphical alternating minimization algorithm, augmented with a consensus term that allows agents to learn the desired structure cooperatively. We allow the system designer to select the number of communication rounds and optimization steps per data point. We characterize the rate of convergence of our algorithm and provide simulations on synthetic datasets.