提出多滞后状态切换模型的可辨识性理论，提升时序模型解释力。
On the Identifiability of Regime-Switching Models with Multi-Lag Dependencies
- 将状态切换模型建模为时序结构混合，通过神经网络设计保证可辨识性
- 在非线性高斯设定下证明状态数与多滞后的可辨识性
- 适用于神经科学、金融和气候等真实数据，增强模型可解释性
可辨识性是深度隐变量模型可解释性的核心，确保参数由数据生成分布唯一确定。然而，对于深层状态切换时间序列，该问题仍研究不足。本文构建了涵盖马尔可夫切换模型（MSMs）和切换动力系统（SDSs）的多滞后状态切换模型（RSMs）通用理论框架。针对MSMs，将模型形式化为时序结构有限混合，并在非线性-高斯设定下证明状态数及多滞后的可辨识性。针对SDSs，通过时序结构实现潜变量的可辨识性（至置换与缩放），进而导出状态依赖潜因果图的可辨识条件（至状态/节点置换）。所有结果在完全无监督设置下成立，依赖可直接通过神经网络设计实现的架构与噪声假设。我们进一步提出一种满足假设的灵活变分估计器，并在合成基准上验证。在神经科学、金融与气候的真实数据集上，可辨识性带来更可信的可解释性分析，对科学发现至关重要。
原文摘要 · Abstract (English)
Identifiability is central to the interpretability of deep latent variable models, ensuring parameterisations are uniquely determined by the data-generating distribution. However, it remains underexplored for deep regime-switching time series. We develop a general theoretical framework for multi-lag Regime-Switching Models (RSMs), encompassing Markov Switching Models (MSMs) and Switching Dynamical Systems (SDSs). For MSMs, we formulate the model as a temporally structured finite mixture and prove identifiability of both the number of regimes and the multi-lag transitions in a nonlinear-Gaussian setting. For SDSs, we establish identifiability of the latent variables up to permutation and scaling via temporal structure, which in turn yields conditions for identifiability of regime-dependent latent causal graphs (up to regime/node permutations). Our results hold in a fully unsupervised setting through architectural and noise assumptions that are directly enforceable via neural network design. We complement the theory with a flexible variational estimator that satisfies the assumptions and validate the results on synthetic benchmarks. Across real-world datasets from neuroscience, finance, and climate, identifiability leads to more trustworthy interpretability analysis, which is crucial for scientific discovery.
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