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

Original language | English (US) |
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Pages (from-to) | 9982-9997 |

Number of pages | 16 |

Journal | Proceedings of Machine Learning Research |

Volume | 151 |

State | Published - 2022 |

Event | 25th International Conference on Artificial Intelligence and Statistics, AISTATS 2022 - Virtual, Online, Spain Duration: Mar 28 2022 → Mar 30 2022 |

### Bibliographical note

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