Semisupervised regression in latent structure networks on unknown manifolds

Aranyak Acharyya, Joshua Agterberg, Michael W. Trosset, Youngser Park, Carey E. Priebe

Research output: Contribution to journalArticlepeer-review

Abstract

Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data.

Original languageEnglish (US)
Article number75
JournalApplied Network Science
Volume8
Issue number1
DOIs
StatePublished - Dec 2023
Externally publishedYes

Keywords

  • Manifold learning
  • Network inference
  • Random dot product graph
  • Regression
  • Vertex covariates

ASJC Scopus subject areas

  • General
  • Computer Networks and Communications
  • Computational Mathematics

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