Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise
This work addresses the challenge of network inference in complex systems with limited data and correlated noise, which is incremental as it builds on existing methods by incorporating specific constraints.
The paper tackles the problem of inferring the underlying network structure in Networked Dynamical Systems (NDS) under conditions of partial observability and spatially colored noise, presenting a feasibility condition for consistent network inference and an algorithm that shows competitive performance across various regimes.
In a Networked Dynamical System (NDS), each node is a system whose dynamics are coupled with the dynamics of neighboring nodes. The global dynamics naturally builds on this network of couplings and it is often excited by a noise input with nontrivial structure. The underlying network is unknown in many applications and should be inferred from observed data. We assume: i) Partial observability -- time series data is only available over a subset of the nodes; ii) Input noise -- it is correlated across distinct nodes while temporally independent, i.e., it is spatially colored. We present a feasibility condition on the noise correlation structure wherein there exists a consistent network inference estimator to recover the underlying fundamental dependencies among the observed nodes. Further, we describe a structure identification algorithm that exhibits competitive performance across distinct regimes of network connectivity, observability, and noise correlation.