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Title: On estimation and inference in latent structure random graphs Authors:  Minh Tang - Johns Hopkins University (United States) [presenting]
Avanti Athreya - Johns Hopkins University (United States)
Youngser Park - Johns Hopkins University (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: A latent structure model (LSM) random graph is defined as a random dot product graph (RDPG) in which the latent position distribution incorporates both probabilistic and geometric constraints, delineated by a family of underlying distributions on some fixed Euclidean space, and a structural support submanifold from which the latent positions for the graph are drawn. For a one-dimensional latent structure model with known structural support, we show how spectral estimates of the latent positions of an RDPG can be used for efficient estimation of the parameters of the LSM. We describe how to estimate or learn the structural support in cases where it is unknown, with an illustrative focus on graphs with latent positions along the Hardy-Weinberg curve. Finally, we use the latent structure model formulation to test bilateral homology in the Drosophila connectome.