B0766
Title: A general latent embedding approach for modeling high-dimensional hyperlinks
Authors: Shihao Wu - University of Michigan, Ann Arbor (United States) [presenting]
Gongjun Xu - University of Michigan (United States)
Ji Zhu - University of Michigan (United States)
Abstract: Hyperlinks encompass polyadic interactions among entities beyond dyadic relations. Despite the growing attention towards hyperlink modeling, most existing methodologies have significant limitations, including a heavy reliance on uniform restrictions of hyperlink orders and the inability to account for repeated observations of identical hyperlinks. We introduce a novel and general latent embedding approach that tackles these challenges through an integration of latent embedding vectors, vertex degree heterogeneity parameters and an order adjusting parameter. We examine identification conditions of the latent embedding vectors and associated parameters and establish convergence rates of their estimators along with asymptotic normality. Particularly, these outcomes are highly contingent upon the order adjusting parameter. We employ a projected gradient ascent algorithm and a universal singular value thresholding initialization to compute the estimators. We perform a comprehensive simulation study that shows the effectiveness of the algorithms and justifies the theoretical findings. Finally, we conduct a real data analysis on the co-citation hypergraph network, further demonstrating the advantages of the latent embedding approach.
