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Activity Number: 245 - SLDS CSpeed 4
Type: Contributed
Date/Time: Wednesday, August 11, 2021 : 10:00 AM to 11:50 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #319041
Title: Spectral Goodness-of-Fit Tests for Complete and Partial Network Data
Author(s): Bolun Liu* and Shane Lubold and Tyler McCormick
Companies: Department of Statistics, University of Washington and Department of Statistics, University of Washington and University of Washington
Keywords: Goodness-of-fit tests; random matrix theory; partial network data; latent space model; exponential random graph model; Aggregated Relational Data

Networks describe the, often complex, relationships between individual actors. In this work, we address the question of how to determine whether a parametric model, such as a stochastic block model or latent space model, fits a dataset well and will extrapolate to similar data. We use recent results in random matrix theory to derive a general goodness-of-fit test for dyadic data. We show that our method, when applied to a specific model of interest, provides an straightforward, computationally fast way of selecting parameters in a number of commonly used network models. For example, we show how to select the dimension of the latent space in latent space models. Unlike other network goodness-of-fit methods, our general approach does not require simulating from a candidate parametric model, which can be cumbersome with large graphs, and eliminates the need to choose a particular set of statistics on the graph for comparison. It also allows us to perform goodness-of-fit tests on partial network data, such as Aggregated Relational Data. We analyze several empirically relevant networks and show that our method leads to improved community detection algorithms.

Authors who are presenting talks have a * after their name.

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