Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs

TL;DR

This paper introduces a passive, efficient method for learning the structure of networked linear dynamical systems driven by non-white inputs, with sample complexity logarithmic in system size, advancing understanding of such systems.

Contribution

It proposes a regularized estimator for learning network interactions from non-white input data and analyzes its sample complexity in different observation regimes.

Findings

Estimator recovers network structure with logarithmic sample complexity

Works for systems driven by unobserved non-white stationary inputs

First analysis of sample complexity for such driven dynamical systems

Abstract

We consider a networked linear dynamical system with $p$ agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval $T$. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval $T$ consists of $n$ i.i.d. observation windows of length $T/n$ (restart and record), and (b) where $T$ is one continuous observation window (consecutive). Using the theory of $M$-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size $p$. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems \emph{driven by unobserved not-white wide-sense stationary (WSS) inputs}.