B1692
Title: Inference and ranking in mixed-membership models
Authors: Sohom Bhattacharya - University of Florida (United States) [presenting]
Abstract: Network data is prevalent in numerous big data applications, including economics and health networks, where it is of prime importance to understand the latent structure of the network. The network is modelled using the degree-corrected mixed membership (DCMM) model. In DCMM model, for each node $i$, there exists a membership vector $\pi_ i = (\pi_i(1), \pi_i(2),\ldots, \pi_i(K))$, where $\pi_i(k)$ denotes the weight that node $i$ puts in community $k$. Novel finite-sample expansion is derived for the $\pi_i(k)$s, which allows for the obtainment of asymptotic distributions and confidence intervals of the membership mixing probabilities and other related population quantities. This fills an important gap in uncertainty quantification on the membership profile. A ranking scheme of the vertices is further developed based on the membership mixing probabilities on certain communities, and relevant statistical inferences are performed. A multiplier bootstrap method is proposed for ranking inference of individual members' profiles with respect to a given community. The theoretical results are complemented with numerical experiments in real data examples.
