Spectral goodness-of-fit tests for complete and partial network data

Shane Lubold, Bolun Liu, Tyler McCormick

Abstract:

Networks describe 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 data set well, and will extrapolate to similar data. We use recent results in random matrix theory to
derive a general goodness-of-fit (GoF) test for dyadic data. We show that our method, when applied to a
specific model of interest, provides a 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 GoF 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 GoF tests on partial network data, such as Aggregated Relational Data. We show with simulations
that our method performs well in many situations of interest. We analyze several empirically relevant
networks and show that our method leads to improved community detection algorithms.