Distributed Estimation of Sparse Inverse Covariances
This work addresses the limitation of batch processing in Gaussian graphical models for distributed data scenarios, offering an incremental improvement for applications like sensor networks or multi-agent systems.
The paper tackles the problem of learning network structures from time-series data collected by distributed agents, proposing a distributed sparse inverse covariance algorithm that enables real-time learning with convergence guarantees and simulation results.
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.