Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families
2026-06-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study how to understand systems that change their behavior over time, like climate seasons or blood sugar levels in diabetic patients. They focus on finding hidden periods (called regimes) where the system acts consistently and how these periods influence cause-and-effect relationships. The paper proves it's possible to identify these hidden regimes and their causal patterns even when the system is complex and noisy. They also create a new method called FlowMSM that helps detect these regimes and the associated causal structures, showing good results on test data and financial examples.
Temporal systemsNon-stationarityMarkov Switching ModelsHidden Markov ModelsCausal discoveryLatent regimesNonlinear dynamicsInstantaneous effectsExponential family noise
Authors
Roel Hulsman, Carles Balsells-Rodas, Sara Magliacane
Abstract
Temporal systems often exhibit non-stationary behaviour, such as seasonal climate variation or glucose fluctuations in patients with type-1 diabetes. One way to model non-stationarity is through discrete latent regimes, i.e., stationary segments of time. Such systems induce a Markov Switching Model (MSM), a class of Hidden Markov Models with autoregressive dependencies among latent regimes and observed variables. Identifying latent regimes is challenging in the presence of frequent regime switches and nonlinear and non-Gaussian dynamics, particularly when there are instantaneous effects between the variables, e.g., due to slow rates of measurements. In this work, we establish the identifiability of both latent regimes and regime-dependent causal structures under temporal regime dependencies, nonlinear lagged and instantaneous effects, and independent noise from the exponential family. Our identifiability theory subsumes non-temporal mixtures of causal models. Furthermore, we introduce FlowMSM, a regime detection framework that can be paired with any stationary causal discovery method to recover regime-dependent causal structures. Experiments on synthetic benchmarks and a financial economics dataset demonstrate the effectiveness of our approach to detect latent regimes and discover causal structures from non-stationary time series.