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Testing for Directed Information Graphs
KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.ORCID-id: 0000-0002-6247-1217
KTH, Skolan för elektroteknik och datavetenskap (EECS), Centra, ACCESS Linnaeus Centre.ORCID-id: 0000-0002-8974-6591
KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre.ORCID-id: 0000-0002-7926-5081
2017 (engelsk)Inngår i: 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), IEEE, 2017, s. 212-219Konferansepaper, Publicerat paper (Fagfellevurdert)
Abstract [en]

In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said processes. Specifically, a k-th order Markov structure is considered for them, and the chosen metric to determine a connection between nodes is the directed information. The hypothesis test is based on the empirically calculated transition probabilities which are used to estimate the directed information. For a single edge, it is proven that the detection probability can be chosen arbitrarily close to one, while the false alarm probability remains negligible. When the test is performed on the whole graph, we derive bounds for the false alarm and detection probabilities, which show that the test is asymptotically optimal by properly setting the threshold test and using a large number of samples. Furthermore, we study how the convergence of the measures relies on the existence of links in the true graph.

sted, utgiver, år, opplag, sider
IEEE, 2017. s. 212-219
Serie
Annual Allerton Conference on Communication Control and Computing, ISSN 2474-0195
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-226276DOI: 10.1109/ALLERTON.2017.8262740ISI: 000428047800030Scopus ID: 2-s2.0-85048130063ISBN: 978-1-5386-3266-6 (tryckt)OAI: oai:DiVA.org:kth-226276DiVA, id: diva2:1198953
Konferanse
55th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2017, Allerton HouseMonticello, United States, 3 October 2017 through 6 October 2017
Merknad

QC 20180419

Tilgjengelig fra: 2018-04-19 Laget: 2018-04-19 Sist oppdatert: 2018-11-14bibliografisk kontrollert

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