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

arXiv: https://arxiv.org/abs/2110.00852 · HTML: https://mlsanity.com/paper/2110.00852/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 2 Oct 2021.

## Builds on (most cited first, 8 of 8)

- [Learning Without Mixing: Towards A Sharp Analysis of Linear System Identification](https://mlsanity.com/paper/1802.08334/) (2018)
- [Finite Time Identification in Unstable Linear Systems](https://mlsanity.com/paper/1710.01852/) (2017)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Learning Sparse Dynamical Systems from a Single Sample Trajectory](https://mlsanity.com/paper/1904.09396/) (2019)
- [Graphical LASSO Based Model Selection for Time Series](https://mlsanity.com/paper/1410.1184/) (2014)
- [Physics Informed Topology Learning in Networks of Linear Dynamical Systems](https://mlsanity.com/paper/1809.10535/) (2018)
- [Bayesian Structure Learning for Stationary Time Series](https://mlsanity.com/paper/1505.03131/) (2015)
- [Exact Topology Learning in a Network of Cyclostationary Processes](https://mlsanity.com/paper/1903.09210/) (2019)

## Built on by (most cited first, 4 of 4)

- [Non-Asymptotic Pointwise and Worst-Case Bounds for Classical Spectrum Estimators](https://mlsanity.com/paper/2303.11908/) (2023)
- [Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphs](https://mlsanity.com/paper/2308.16859/) (2023)
- [Causal Structure Recovery of Linear Dynamical Systems: An FFT based Approach](https://mlsanity.com/paper/2309.02571/) (2023)
- [Learning Networks from Wide-Sense Stationary Stochastic Processes](https://mlsanity.com/paper/2412.03768/) (2024)

## Abstract (arXiv)

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 driven by unobserved not-white wide-sense stationary (WSS) inputs.