Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs
This work addresses the challenge of efficiently inferring network structures from data in dynamical systems, which is incremental as it extends analysis to non-white exogenous inputs.
The paper tackles the problem of learning the underlying graph of interactions in networked linear dynamical systems from nodal trajectory observations, and presents a regularized non-casual consistent estimator that recovers these interactions in a time-interval logarithmic in system size, with sample complexity analyzed for both restart-and-record and consecutive observation regimes.
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}.