The identifiability of latent variable models has received increasing attention due to its relevance in interpretability and out-of-distribution generalisation. In this work, we study the identifiability of Switching Dynamical Systems, taking an initial step toward extending identifiability analysis to sequential latent variable models. We first prove the identifiability of Markov Switching Models, which commonly serve as the prior distribution for the continuous latent variables in Switching Dynamical Systems. We present identification conditions for first-order Markov dependency structures, whose transition distribution is parametrised via non-linear Gaussians. We then establish the identifiability of the latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations, by leveraging identifiability analysis techniques from identifiable deep latent variable models. We finally develop estimation algorithms for identifiable Switching Dynamical Systems. Throughout empirical studies, we demonstrate the practicality of identifiable Switching Dynamical Systems for segmenting high-dimensional time series such as videos, and showcase the use of identifiable Markov Switching Models for regime-dependent causal discovery in climate data.

翻译：潜变量模型的可辨识性因其在可解释性与分布外泛化中的重要性而日益受到关注。本研究探讨切换动态系统的可辨识性，为将可辨识性分析扩展至序列潜变量模型迈出初步步伐。我们首先证明了马尔可夫切换模型的可辨识性，该模型通常作为切换动态系统中连续潜变量的先验分布。我们提出了针对一阶马尔可夫依赖结构的辨识条件，其转移分布通过非线性高斯模型进行参数化。随后，通过借鉴可辨识深度潜变量模型的分析技术，我们确立了切换动态系统中潜变量与非线性映射在仿射变换意义下的可辨识性。最后，我们为可辨识切换动态系统开发了估计算法。在实证研究中，我们展示了可辨识切换动态系统在高维时间序列（如视频）分割中的实用性，并展现了可辨识马尔可夫切换模型在气候数据中基于状态机制的因果发现中的应用价值。