  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.
