In the realm of interpretability and out-of-distribution generalisation, the identifiability of latent variable models has emerged as a captivating field of inquiry. In this work, we delve into the identifiability of Switching Dynamical Systems, taking an initial stride 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：在可解释性和分布外泛化领域，潜变量模型的可辨识性已成为一个引人入胜的研究方向。本文深入探讨切换动力系统的可辨识性，迈出了将可辨识性分析拓展至序列潜变量模型的第一步。我们首先证明了马尔可夫切换模型的可辨识性——该模型常作为切换动力系统中连续潜变量的先验分布。我们给出了基于非线性高斯参数化转移分布的一阶马尔可夫依赖结构的辨识条件。随后，通过借鉴可辨识深度潜变量模型的分析技术，我们建立了切换动力系统中潜变量与非线性映射在仿射变换下的可辨识性。最终，我们为可辨识切换动力系统开发了估计算法。通过实证研究，我们展示了可辨识切换动力系统在分割高维时间序列（如视频）中的实用性，并阐释了可辨识马尔可夫切换模型在气候数据中进行状态依赖因果发现的应用。