Regime-Specific Causal Discovery from a Variance-based Markov-Switching-Model

Temporal causal discovery typically assumes that a single causal structure and set of mechanisms govern an entire time series. In many systems, however, the process repeatedly switches among unobserved regimes, and different regimes may have different causal mechanisms and lagged parent sets. Pooling observations across such regimes may therefore obscure genuine causal relations. We study the recovery of regime-specific lagged causal structure when the regimes themselves are latent and recurrent. We propose the Variance-based Markov-Switching-Model (VB-MSM), in which a shared latent Markov state selects regime-specific nonlinear conditional mechanisms. We measure the contribution of each candidate parent through its complete edge function, i.e., an edge is considered active when its contribution to the regime-conditional mean varies with its input. Thus our method is invariant of the specific parameterization. We show that removing a true parent changes the regime-conditional mean under common causal assumptions. VB-MSM combines nonlinear mechanism learning with exact forward–backward inference over the finite-state regime process in an EM-style update. On nonlinear switching benchmarks, it accurately recovers regime-specific graphs, latent regimes, and intervention effects. Comparisons with baseline methods like iMSM and FlowMSM+RHINO show its strengths across different mechanisms. Experiments with added noise also retain strong recovery at native and reduced sample lengths.