Maximum Likelihood Estimation and Graph Matching in Errorfully Observed Networks. Issue 4 (2nd October 2021)

• Record Type: Journal Article
• Authors: Arroyo, Jesús; Sussman, Daniel L.; Priebe, Carey E.; Lyzinski, Vince
• Is Part Of: Journal of computational and graphical statistics. Volume 30:Issue 4(2021)
• Page Start: 1111
• Page End: 1123
• Publication Date: 2021-10-02
• Subjects: Consistency -- Corrupting channel -- Graph matchability; Mathematical statistics -- Data processing -- Periodicals; Mathematical statistics -- Graphic methods -- Periodicals; 519.50285
• DOI: 10.1080/10618600.2021.1872582
• Languages: English
• ISSNs: 1061-8600

Abstract

Abstract: Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study this problem from a statistical framework in which one of the graphs is an errorfully observed copy of the other. We introduce a corrupting channel model, and show that in this model framework, the solution to the graph matching problem is a maximum likelihood estimator (MLE). Necessary and sufficient conditions for consistency of this MLE are presented, as well as a relaxed notion of consistency in which a negligible fraction of the vertices need not be matched correctly. The results are used to study matchability in several families of random graphs, including edge independent models, random regular graphs, and small-world networks. We also use these results to introduce measures of matching feasibility, and experimentally validate the results on simulated and real-world networks. Supplemental files for this article are available online.