Online change point detection for weighted and directed random dot product graphs

Marenco, Bernardo - Bermolen, Paola - Fiori, Marcelo - Larroca, Federico - Mateos, Gonzalo

Resumen:

Given a sequence of random (directed and weighted) graphs, we address the problem of online monitoring and detection of changes in the underlying data distribution. Our idea is to endow sequential change-point detection (CPD) techniques with a graph representation learning substrate based on the versatile Random Dot Product Graph (RDPG) model. We consider efficient, online updates of a judicious monitoring function, which quantifies the discrepancy between the streaming graph observations and the nominal RDPG. This reference distribution is inferred via spectral embeddings of the first few graphs in the sequence. We characterize the distribution of this running statistic to select thresholds that guarantee error-rate control, and under simplifying approximations we offer insights on the algorithm’s detection resolution and delay. The end result is a lightweight online CPD algorithm, that is also explainable by virtue of the well-appreciated interpretability of RDPG embeddings. This is in stark contrast with most existing graph CPD approaches, which either rely on extensive computation, or they store and process the entire observed time series. An apparent limitation of the RDPG model is its suitability for undirected and unweighted graphs only, a gap we aim to close here to broaden the scope of the CPD framework. Unlike previous proposals, our non-parametric RDPG model for weighted graphs does not require a priori specification of the weights’ distribution to perform inference and estimation. This network modeling contribution is of independent interest beyond CPD. We offer an open-source implementation of the novel online CPD algorithm for weighted and direct graphs, whose effectiveness and efficiency are demonstrated via (reproducible) synthetic and real network data experiments


Detalles Bibliográficos
2022
Work in this paper is supported in part by ANII (grant FMV 3 2018 1 148149) and the NSF (awards CCF-1750428, CCF-1934962 and ECCS-1809356). Part of the results in this paper were submitted to the 2021 EUSIPCO and Asilomar Conferences
Data models
Monitoring
Delays
Computational modeling
Symmetric matrices
Probability
Information processing
Online change-point detection
Graph representation learning
Node embeddings
Random dot product graphs
Inglés
Universidad de la República
COLIBRI
https://ieeexplore.ieee.org/document/9706333
https://hdl.handle.net/20.500.12008/30974
Acceso abierto
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)

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