Weighted Random Dot Product Graphs
Bernardo Marenco, Paola Bermolen, Marcelo Fiori, Federico Larroca, Gonzalo Mateos

TL;DR
This paper extends the Random Dot Product Graph model to weighted graphs, allowing for nuanced modeling of edge weights and providing statistical guarantees for latent position estimation.
Contribution
It introduces a nonparametric weighted RDPG model with theoretical guarantees and a generative framework for weighted graphs, broadening the applicability of RDPG models.
Findings
Consistent and asymptotically normal estimator for latent positions.
Framework for generating weighted graphs with prescribed properties.
Enhanced discrimination of weight distributions beyond mean comparison.
Abstract
Modeling of intricate relational patterns has become a cornerstone of contemporary statistical research and related data science fields. Networks, represented as graphs, offer a natural framework for this analysis. This paper extends the Random Dot Product Graph (RDPG) model to accommodate weighted graphs, markedly broadening the model's scope to scenarios where edges exhibit heterogeneous weight distributions. We propose a nonparametric weighted (W)RDPG model that assigns a sequence of latent positions to each node. Inner products of these nodal vectors specify the moments of their incident edge weights' distribution via moment-generating functions. In this way, and unlike prior art, the WRDPG can discriminate between weight distributions that share the same mean but differ in other higher-order moments. We derive statistical guarantees for an estimator of the nodal's latent positions…
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Taxonomy
TopicsComplex Network Analysis Techniques · Advanced Graph Neural Networks · Bayesian Methods and Mixture Models
