A0433
Title: Simultaneous estimation of connectivity and dimensionality in samples of networks
Authors: Wenlong Jiang - University of Pittsburgh (United States)
Jesus Arroyo - Texas A&M University (United States)
Christopher McKennan - University of Pittsburgh (United States)
Joshua Cape - University of Wisconsin, Madison (United States) [presenting]
Abstract: A method is proposed to simultaneously estimate a latent connectivity matrix and its embedding dimensionality (rank) after first pre-estimating the number of communities and node cluster memberships. The method is formulated as a convex optimization problem and solved using an alternating direction method of multipliers algorithm. Estimation error bounds are established under the Frobenius norm and nuclear norm for settings in which observable networks have blockmodel structure. Numerical studies empirically demonstrate the accuracy of our method even when node block memberships are imperfectly recovered. When exact membership recovery is possible and dimensionality is much smaller than the number of communities, the method outperforms averaging-based methods for estimating connectivity and dimensionality. Analysis of a primate brain dataset demonstrates that posited connectivity is not necessarily full rank in practice, illustrating the need for flexible methodology.
