Identifying Nonstationary Causal Structures with High-Order Markov Switching Models

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to nonstationary time series with time-dependent effects or heterogeneous noise. In this work we address nonstationarity via regime-dependent causal structures. We first establish identifiability for high-order Markov Switching Models, which provide the foundations for identifiable regime-dependent causal discovery. Our empirical studies demonstrate the scalability of our proposed approach for high-order regime-dependent structure estimation, and we illustrate its applicability on brain activity data.

On the Identifiability of Markov Switching Models

Identifiability of latent variable models has recently gained interest in terms of its applications to interpretability or out of distribution generalisation. In this work, we study identifiability of Markov Switching Models as a first step towards extending recent results to sequential latent variable models. We present identifiability conditions within first-order Markov dependency structures, and parametrise the transition distribution via non-linear Gaussians. Our experiments showcase the applicability of our approach for regime-dependent causal discovery and high-dimensional time series segmentation.