ADDITIVE SEPARABLE GRAPHON MODELS
Keywords: graphon, subgraph counts, low-rank connecting probability matrix, nonparametric statistics, network analysis
TL;DR: A new additive separable graphon model, capable of generating a low-rank connection probability matrix for network data, is proposed along with efficient estimation methods
Abstract: The graphon function is fundamental to modeling exchangeable graphs, which form the basis for a wide variety of networks. In this paper, we introduce the additive separable model as a parsimonious representation of the graphon, capable of generating a low-rank connection probability matrix for network data. This model effectively addresses the well-known identification challenges associated with graphon functions. We develop an efficient estimation approach that leverages subgraph counts to estimate the low-rank connection matrix and uses interpolation to recover the graphon functions, achieving the minimax optimal estimation rate. We provide the convergence rate of our method, and validate its computational efficiency and estimation accuracy through comprehensive simulation studies.
Primary Area: learning on graphs and other geometries & topologies
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Submission Number: 10611
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