Using Cyclic Structure to Improve Inference on Networks

• Activity Number: 80 - Graphical Models and Causal Inference
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Behnaz Moradijamei* and Michael Higgins
• Companies: Kansas State University and Kansas State University
• Keywords: Networks inference; Goodness-of-fit test; Hypothesis testing; Network; Community Detection; Stochastic block model

Abstract

Identifying communities is a critical task in the analysis of large datasets often modeled by networks. Statistical models such as the stochastic block model have proven to be successful in explaining the structure of communities in real-world network data. In this work, we develop a goodness-of-fit test to examine the existence of communities by using a distinguishing property in networks: cyclic structures are more prevalent within communities than across them. We utilize these structures through the use of our novel method, renewal non-backtracking random walk (RNBRW) to the existing goodness-of-fit test. RNBRW is an important variant of random walk in which the walk is prohibited from returning back to a node in exactly two steps and terminates and restarts once it completes a loop. We investigate the use of RNBRW to improve the performance of existing goodness-of-fit tests for community detection algorithms that is based on the spectral properties of the adjacency matrix.