On the Identifiability of Switching Dynamical Systems
This work addresses interpretability and out-of-distribution generalization for sequential latent variable models, representing an incremental extension of identifiability analysis to this domain.
The paper tackles the identifiability of Switching Dynamical Systems, proving identifiability for Markov Switching Models and establishing identifiability of latent variables and non-linear mappings up to affine transformations, with empirical demonstrations on video segmentation and climate data.
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.