### Abstract

Complex systems can often be understood via a graph abstraction where nodes represent individual components and edges represent input/output relations among them. Recovering the network structure of a complex system from noninvasively observed data plays a central role in many areas of science. A classic approach to this problem is Granger causality. For strictly causal linear dynamic systems, Granger causality guarantees a consistent reconstruction of the network. However, it is a well-established fact that Granger causality, and analogous methods, lead to the inference of spurious links in the presence of direct feedthroughs. On the other hand, graphical model approaches can deal successfully with static operators in acyclic structures. Indeed, in those cases, graphical model tools guarantee a consistent network reconstruction, apart from pathological conditions associated with very specific values of the system parameters. When these pathological conditions do not occur, borrowing terminology from the theory of graphical models, the network is said to be faithful to its graph representation. We discuss the notion of faithfulness and adapt it to the more general case of networks of dynamic systems, in order to combine the main idea behind Granger causality with graphical model techniques. We provide an algorithm which, under faithfulness, has theoretical guarantees for the reconstruction of a large class of linear models containing both direct feedthroughs and feedback loops.

Original language | English (US) |
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Title of host publication | 2019 American Control Conference, ACC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Number of pages | 1 |

ISBN (Electronic) | 9781538679265 |

State | Published - Jul 1 2019 |

Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: Jul 10 2019 → Jul 12 2019 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2019-July |

ISSN (Print) | 0743-1619 |

### Conference

Conference | 2019 American Control Conference, ACC 2019 |
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Country | United States |

City | Philadelphia |

Period | 7/10/19 → 7/12/19 |

### Fingerprint

### Cite this

*2019 American Control Conference, ACC 2019*[8814776] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc..

**A brief explanation of the issue of faithfulness and link orientation in network reconstruction.** / Dimovska, Mihaela; Materassi, Donatello.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2019 American Control Conference, ACC 2019.*, 8814776, Proceedings of the American Control Conference, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., 2019 American Control Conference, ACC 2019, Philadelphia, United States, 7/10/19.

}

TY - GEN

T1 - A brief explanation of the issue of faithfulness and link orientation in network reconstruction

AU - Dimovska, Mihaela

AU - Materassi, Donatello

PY - 2019/7/1

Y1 - 2019/7/1

N2 - Complex systems can often be understood via a graph abstraction where nodes represent individual components and edges represent input/output relations among them. Recovering the network structure of a complex system from noninvasively observed data plays a central role in many areas of science. A classic approach to this problem is Granger causality. For strictly causal linear dynamic systems, Granger causality guarantees a consistent reconstruction of the network. However, it is a well-established fact that Granger causality, and analogous methods, lead to the inference of spurious links in the presence of direct feedthroughs. On the other hand, graphical model approaches can deal successfully with static operators in acyclic structures. Indeed, in those cases, graphical model tools guarantee a consistent network reconstruction, apart from pathological conditions associated with very specific values of the system parameters. When these pathological conditions do not occur, borrowing terminology from the theory of graphical models, the network is said to be faithful to its graph representation. We discuss the notion of faithfulness and adapt it to the more general case of networks of dynamic systems, in order to combine the main idea behind Granger causality with graphical model techniques. We provide an algorithm which, under faithfulness, has theoretical guarantees for the reconstruction of a large class of linear models containing both direct feedthroughs and feedback loops.

AB - Complex systems can often be understood via a graph abstraction where nodes represent individual components and edges represent input/output relations among them. Recovering the network structure of a complex system from noninvasively observed data plays a central role in many areas of science. A classic approach to this problem is Granger causality. For strictly causal linear dynamic systems, Granger causality guarantees a consistent reconstruction of the network. However, it is a well-established fact that Granger causality, and analogous methods, lead to the inference of spurious links in the presence of direct feedthroughs. On the other hand, graphical model approaches can deal successfully with static operators in acyclic structures. Indeed, in those cases, graphical model tools guarantee a consistent network reconstruction, apart from pathological conditions associated with very specific values of the system parameters. When these pathological conditions do not occur, borrowing terminology from the theory of graphical models, the network is said to be faithful to its graph representation. We discuss the notion of faithfulness and adapt it to the more general case of networks of dynamic systems, in order to combine the main idea behind Granger causality with graphical model techniques. We provide an algorithm which, under faithfulness, has theoretical guarantees for the reconstruction of a large class of linear models containing both direct feedthroughs and feedback loops.

UR - http://www.scopus.com/inward/record.url?scp=85072273522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072273522&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072273522

T3 - Proceedings of the American Control Conference

BT - 2019 American Control Conference, ACC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -