Markov-Switching State-Space Models with Applications to Neuroimaging

TL;DR

This paper introduces new statistical methods for Markov-switching state-space models, enabling efficient analysis of high-dimensional neuroimaging data like EEG signals, with practical algorithms and a MATLAB toolbox.

Contribution

It develops novel maximum likelihood, EM, and bootstrap techniques tailored for high-dimensional, massive spatio-temporal data in neuroimaging applications.

Findings

Effective initialization and acceleration of EM algorithm.

Successful application to EEG epilepsy and motor imagery data.

Open-source MATLAB toolbox implementation.

Abstract

State-space models (SSM) with Markov switching offer a powerful framework for detecting multiple regimes in time series, analyzing mutual dependence and dynamics within regimes, and asserting transitions between regimes. These models however present considerable computational challenges due to the exponential number of possible regime sequences to account for. In addition, high dimensionality of time series can hinder likelihood-based inference. This paper proposes novel statistical methods for Markov-switching SSMs using maximum likelihood estimation, Expectation-Maximization (EM), and parametric bootstrap. We develop solutions for initializing the EM algorithm, accelerating convergence, and conducting inference that are ideally suited to massive spatio-temporal data such as brain signals. We evaluate these methods in simulations and present applications to EEG studies of epilepsy and of motor imagery. All proposed methods are implemented in a MATLAB toolbox available at https://github.com/ddegras/switch-ssm.