A0969
Title: Testing for repeated motifs and hierarchical structure in stochastic block models
Authors: Al-Fahad Al-Qadhi - University of Maryland (United States)
Keith Levin - University of Wisconsin (United States)
Vince Lyzinski - University of Maryland, College Park (United States) [presenting]
Abstract: The rise in complexity of network data in neuroscience, social networks, and protein-protein interaction networks has been accompanied by several efforts to model and understand these data at different scales. A key multiscale network modeling technique posits a hierarchical structure in the network, and by treating networks as multiple levels of subdivisions with shared statistical properties, smaller subgraph primitives can be efficiently discovered with manageable complexity. One such example of hierarchical modeling is the hierarchical stochastic block model, which seeks to model complex networks as being composed of community structures repeated across the network. Incorporating repeated structure allows for parameter tying across communities in the SBM, reducing the model complexity compared to the traditional block model. A framework is formulated for testing for repeated motif hierarchical structure in the stochastic block model framework. A model is described that naturally expresses networks as a hierarchy of sub-networks with a set of motifs repeating across them, and the practical utility of the test is demonstrated through theoretical analysis, extensive simulation, and real data.
