Establish consistency of RCBNB-MB

Establish whether the RCBNB-MB algorithm consistently converges to the ground-truth regime assignments and regime-specific window causal graphs as the sample size increases.

Background

RCBNB-MB alternates between estimating regime-specific window causal graphs with CBNB and updating regime assignments using Markov-blanket-based prediction. The paper proves recovery of the causal graphs when regime assignments are correct and describes empirical performance showing that the algorithm is often close to the ground truth. However, the alternating optimization procedure is not accompanied by a consistency theorem guaranteeing convergence to the ground-truth assignments and graphs. Establishing such a guarantee would provide a theoretical foundation for the complete joint regime-discovery procedure rather than only for its individual steps.

References

While there is no theoretical guarantee that RCBNB-MB consistently converges to the ground truth, empirical results in Section~\ref{sec:exper} show that its outputs are often close to the ground truth in the majority of cases.

— Beyond Stationarity in Time Series: Discovering Causal Structures and Latent Regimes via Markov Blankets  (2609.05150 - Zan et al., 4 Sep 2026) in Section “RCBNB-MB: an algorithm for causal discovery from multiple regimes”