Recursive Network Estimation From Binary-Valued Observation Data

TL;DR

This paper introduces a recursive method for estimating network structures from binary data generated by nonlinear dynamics, ensuring stability and identifiability under Gaussian disturbances, with proven convergence and robustness.

Contribution

It develops a novel recursive estimation algorithm for binary-valued network data with theoretical guarantees and practical robustness.

Findings

Algorithm is strongly consistent and converges reliably.

Estimation is robust to small unmodeled factors.

Conditions for stability and identifiability are established.

Abstract

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which agents exchange and display binary outputs. Sufficient conditions are given to ensure stability of the observation sequence and identifiability of the system parameters. It is shown that stability and identifiability can be guaranteed under the assumption of independent standard Gaussian disturbances. Via a maximum likelihood approach, the estimation problem is transformed into an optimization problem, and it is verified that its solution is the true parameter vector under the independent standard Gaussian assumption. A recursive algorithm for the estimation problem is then proposed based on stochastic approximation techniques. Its strong consistency is established and convergence rate analyzed. Finally, numerical simulations are conducted to illustrate the results and to show that the proposed algorithm is insensitive to small unmodeled factors.