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：时间系统常呈现非平稳特性，例如季节性气候波动或1型糖尿病患者的血糖变化。建模非平稳性的一种方法是通过离散潜在状态（即时间上的平稳区间）。此类系统可导出马尔可夫切换模型（MSM）——一种隐马尔可夫模型，其中潜在状态与观测变量间存在自回归依赖关系。在频繁状态切换、非线性非高斯动态特性下识别潜在状态颇具挑战性，尤其当变量间存在瞬时效应时（例如因测量速率缓慢所致）。本研究建立了在时间状态依赖、非线性滞后效应与瞬时效应、以及指数族独立噪声条件下，潜在状态及其依赖因果结构的可识别性理论。该可识别性理论概括了非时间混合因果模型。此外，我们提出了FlowMSM框架——该框架可配合任意平稳因果发现方法，用于恢复状态依赖的因果结构。在合成基准与金融经济学数据集上的实验表明，本方法能从非平稳时间序列中有效检测潜在状态并发现因果结构。