Establish theoretical guarantees for outlier detection in non-stationary data streams

Establish rigorous theoretical guarantees for outlier detection in non-stationary data streams, particularly for approaches based on sliding-window techniques, ensemble methods, and data weighting, to characterize their performance and error control under distribution shift.

Background

The paper studies one-pass streaming outlier detection under non-stationarity and proposes SONAR, an SGD-based variant of OCSVM with strong convexity and changepoint detection. In surveying prior work on outlier detection in changing environments, the authors note that many practical approaches—such as sliding-window methods, ensembles, and data weighting—lack rigorous theoretical analysis in non-stationary settings.

This gap motivates the development of formal guarantees that can bound Type I and Type II errors or otherwise quantify performance when distributions shift over time. The authors’ method provides such guarantees for their specific approach, but the broader landscape of non-stationary outlier detection methods remains largely unanalyzed.

References

Prior approaches to outlier detection in non-stationary data streams consist of sliding-window techniques, ensemble methods, and data weighting. However, theoretical guarantees largely remain unknown for this challenging setting.

— An Efficient Variant of One-Class SVM with Lifelong Online Learning Guarantees  (2512.11052 - Suk et al., 11 Dec 2025) in Section 2, Related Works (Outlier Detection in Changing Environments)

We do not evaluate temporal concept drift within a domain or a stream, nor non-stationarity within a single long series, such as an anomalous pattern that becomes normal over time. Nothing in the method precludes these cases, since RAMSAD retrieves per segment and aggregates segment matches into a series ranking, so later segments of an evolving series are embedded and retrieved afresh and the recommendation can change as they accumulate. We present this as a direction for future work, together with a streaming evaluation protocol, and not as a claim supported by our experiments.

— Retrieval Over Training: Similarity search-based Model Selection for Time Series Anomaly Detection  (2610.20243 - Panourgias et al., 14 Oct 2026) in Appendix, Section "Additional Discussions," subsection "Limitations" (Temporal concept drift and streaming)