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Activity Number: 75 - Probability and Statistics
Type: Contributed
Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract #301676 Presentation
Title: Estimation in the Popularity Adjusted Block Model
Author(s): Ramchandra Rimal* and Marianna Pensky
Companies: Univ. of Central Florida and University of Central Florida
Keywords: Community Detection; Stochastic Block Model; Degree-Corrected Block Model; Popularity Adjusted Block Model; Oracle Inequality; Estimation error

Consider a network with its adjacency matrix A_(ij) ~ Ber(P_(ij)). We consider the Popularity Adjusted Block model (PABM) introduced by Sengupta and Chen(2018). We argue that the main appeal of the PABM is the flexibility of the spectral properties of the graph which makes the PABM an attractive choice for modeling networks that appear in biological sciences. We expand the theory of PABM to the case of an arbitrary number of communities which possibly grows with a number of nodes in the network and is not assumed to be known. We derive the estimators of the probability matrix P and the community structure. We further provide non-asymptotic upper bounds for the estimation and the clustering errors.

Authors who are presenting talks have a * after their name.

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