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August 2019 The Geometry of Continuous Latent Space Models for Network Data
Anna L. Smith, Dena M. Asta, Catherine A. Calder
Statist. Sci. 34(3): 428-453 (August 2019). DOI: 10.1214/19-STS702

Abstract

We review the class of continuous latent space (statistical) models for network data, paying particular attention to the role of the geometry of the latent space. In these models, the presence/absence of network dyadic ties are assumed to be conditionally independent given the dyads’ unobserved positions in a latent space. In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic ties. Specifically, these models naturally capture homophilous tendencies and triadic clustering, among other common properties of observed networks. In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks arising from these models via intuition and simulation. Finally, we discuss results from spectral graph theory that allow us to explore the role of the geometry of the latent space, independent of network size. We conclude with conjectures about how these results might be used to infer the appropriate latent space geometry from observed networks.

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Anna L. Smith. Dena M. Asta. Catherine A. Calder. "The Geometry of Continuous Latent Space Models for Network Data." Statist. Sci. 34 (3) 428 - 453, August 2019. https://doi.org/10.1214/19-STS702

Information

Published: August 2019
First available in Project Euclid: 11 October 2019

zbMATH: 07162131
MathSciNet: MR4017522
Digital Object Identifier: 10.1214/19-STS702

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.34 • No. 3 • August 2019
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