Spectral embedding of inhomogeneous Poisson processes on multiplex networks

TL;DR

This paper introduces a spectral embedding method for inhomogeneous Poisson processes on multiplex networks, providing theoretical guarantees and demonstrating effectiveness through simulations and real data analysis.

Contribution

It develops a novel spectral embedding approach for multiplex network point processes with theoretical consistency and asymptotic normality results.

Findings

Spectral embedding accurately estimates latent positions in multiplex networks.

The method is consistent as network size and time resolution increase.

Real data analysis confirms practical effectiveness.

Abstract

In many real-world networks, data on the edges evolve in continuous time, naturally motivating representations based on point processes. Heterogeneity in edge types further gives rise to multiplex network point processes. In this work, we propose a model for multiplex network data observed in continuous-time. We establish two-to-infinity norm consistency and asymptotic normality for spectral-embedding-based estimation of the model parameters as both network size and time resolution increase. Drawing inspiration from random dot product graph models, each edge intensity is expressed as the inner product of two low-dimensional latent positions: one dynamic and layer-agnostic, the other static and layer-dependent. These latent positions constitute the primary objects of inference, which is conducted via spectral embedding methods. Our theoretical results are established under a histogram estimator of the network intensities and provide justification for applying a doubly unfolded adjacency spectral embedding method for estimation. Simulations and real-data analyses demonstrate the effectiveness of the proposed model and inference procedure.