Anomaly detection in autoregressive networks

[2608.15047] Anomaly detection in autoregressive networks Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Methodology arXiv:2608.15047 (stat) COVID-19 e-print Important: e-prints posted on arXiv are not peer-reviewed by arXiv; they should not be relied upon without context to guide clinical practice or health-related behavior and should not be reported in news media as established information without consulting multiple experts in the field. [Submitted on 15 Aug 2026] Title: Anomaly detection in autoregressive networks Authors: Xianghe Zhu View a PDF of the paper titled Anomaly detection in autoregressive networks, by Xianghe Zhu View PDF HTML (experimental) Abstract: We study anomaly detection in temporally dependent network sequences. Methods based only on adjacency matrices, which are widely used for static networks, can miss changes in the way edges evolve. We instead represent each pair of consecutive networks by separate formation and dissolution event matrices, and embed the resulting matrix sequences using unfolded adjacency spectral embedding. Comparing these embeddings against a stationary baseline yields vertex- and network-level statistics that detect an anomalous transition and identify whether it involves formation, dissolution, or both. For autoregressive random dot product graphs, we establish uniform rowwise consistency of the transition-event embeddings and derive high-probability guarantees for vertex- and network-level detection and exact recovery of the anomalous vertex set. The theory separates a vertex's own displacement from interference caused by other vertices and from autoregressive memory. We quantify the memory left by an earlier anomaly, show that it decays geometrically after the transition mechanism returns to baseline, and give conditions under which it is negligible. A degree-corrected stochastic block model extension gives exact community recovery and provides community-reassignment, centre-shift, split, and merge anomaly statistics with high-probability detection and recovery guarantees. Simulations and applications to an international trade dataset and a primary-school contact network illustrate the performance of the proposed method, revealing a dissolution-driven trade decline followed by formation-driven recovery during COVID-19 and temporary merge-type mixing between school classes. Subjects: Methodology (stat.ME) Cite as: arXiv:2608.15047 [stat.ME] (or arXiv:2608.15047v1 [stat.ME] for this version) https://doi.org/10.48550/arXiv.2608.15047 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Xianghe Zhu [ view email ] [v1] Sat, 15 Aug 2026 05:17:33 UTC (257 KB) Full-text links: Access Paper: View a PDF of the paper titled Anomaly detection in autoregressive networks, by Xianghe Zhu View PDF HTML (experimental) TeX Source view license Current browse context: stat.ME < prev | next > new | recent | 2026-08 Change to browse by: stat References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... 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