B0715
Title: Statistical inference for community structure in weighted networks
Authors: Mingao Yuan - North Dakota State University (United States) [presenting]
Zuofeng Shang - New Jersey Institute of Technology (United States)
Abstract: Community detection refers to the problem of clustering the nodes of a network into groups. Existing inferential methods for community structure mainly focus on unweighted binary networks. Many real-world networks are nonetheless weighted, and a common practice is to dichotomize a weighted network to an unweighted one known to result in information loss. Literature on hypothesis testing in the latter situation is still missing. The problem of testing the existence of community structure is studied in weighted networks. The contributions are threefold: (a) the (possibly infinite-dimensional) exponential family is used to model the weights and derive the sharp information-theoretic limit for the existence of a consistent test. Within the limit, any test is inconsistent, and beyond the limit, a useful, consistent test is proposed. (b) Based on the information-theoretic limits, the first formal way to quantify the loss of information incurred by dichotomizing weighted graphs into unweighted graphs in the context of hypothesis testing is provided. (c) Several new and practically useful test statistics are proposed. A simulation study shows that the proposed tests have good performance. Finally, the proposed tests are applied to an animal social network.
