Distributed Estimation of Sparse Inverse Covariances

TL;DR

This paper introduces a distributed online algorithm for learning sparse inverse covariance matrices, enabling multiple agents to cooperatively infer network structures from time-series data in real-time.

Contribution

It presents a novel distributed, online graphical alternating minimization algorithm with consensus, allowing scalable real-time structure learning across multiple agents.

Findings

Algorithm converges at a quantifiable rate.

Effective in synthetic data simulations.

Supports adjustable communication and computation trade-offs.

Abstract

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.