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.

翻译：时间系统常表现出非平稳行为，例如季节性气候波动或1型糖尿病患者的血糖波动。通过离散潜在机制（即平稳时间片段）可对非平稳性进行建模。此类系统衍生出马尔可夫切换模型——一类隐马尔可夫模型，其潜在机制与观测变量间存在自回归依赖关系。当出现频繁的机制切换、非线性与非高斯动态特性，特别是变量间存在瞬时效应（例如由低测量频率导致）时，识别潜在机制具有挑战性。本研究在时间机制依赖性、非线性滞后与瞬时效应、及指数族分布独立噪声条件下，建立了潜在机制及其依赖因果结构的可辨识性。我们的可辨识性理论涵盖了非时间混合因果模型。此外，我们提出FlowMSM机制检测框架，该框架可与任意平稳因果发现方法结合，恢复机制依赖的因果结构。在合成基准数据集与金融经济学数据集上的实验表明，该方法能有效从非平稳时间序列中检测潜在机制并发现因果结构。