Formal guarantees for restarting continuous monitoring

Prove formal detection and false-alarm guarantees for the procedure that restarts the frozen context encoder and Shiryaev–Roberts statistic after each detected alarm in order to monitor sequences containing multiple regime changes.

Background

The formal analysis in the paper targets a single change-point θ\theta. For continuous monitoring with multiple regime changes, the proposed extension is to restart the context estimation and reset the Shiryaev–Roberts statistic after each alarm.

This restart procedure is only sketched and is not analyzed in the paper. Establishing formal guarantees would require analyzing the interaction between repeated context re-estimation, statistic resetting, subsequent change-points, and false-alarm control across monitoring episodes.

References

Finally, Algorithm~\ref{alg:sr-detection} targets a single $\theta$. Extending it to continuous monitoring by restarting the context and SR statistic at each alarm, as sketched in Appendix~\ref{app:algorithm}, but not analysed, and proving formal guarantees for the restart procedure remain open.

— Change Detection in Probability Flow ODE: Online Testing in Diffusion Latent Spaces  (2608.22807 - Kraevskiy et al., 24 Aug 2026) in Section 6, “Conclusion and Future Directions”