Maximum Likelihood Estimation of Dynamic Sub-Networks with Missing Data

TL;DR

This paper presents a novel maximum likelihood estimation method for identifying sub-networks within large interconnected systems, reducing computational complexity and preserving privacy by relying only on local measurements under certain topological conditions.

Contribution

It introduces a new approach for sub-network identification that avoids full network estimation and leverages local data, under specific topological assumptions.

Findings

Method reduces computational complexity significantly.

Approach enhances privacy by avoiding sharing internal data.

Demonstrated effectiveness through numerical examples.

Abstract

Maximum likelihood estimation is effective for identifying dynamical systems, but applying it to large networks becomes computationally prohibitive. This paper introduces a maximum likelihood estimation method that enables identification of sub-networks within complex interconnected systems without estimating the entire network. The key insight is that under specific topological conditions, a sub-network's parameters can be estimated using only local measurements: signals within the target sub-network and those in the directly connected to the so-called separator sub-network. This approach significantly reduces computational complexity while enhancing privacy by eliminating the need to share sensitive internal data across organizational boundaries. We establish theoretical conditions for network separability, derive the probability density function for the sub-network, and demonstrate the method's effectiveness through numerical examples.