Statistique - Probabilités - Optimisation et Contrôle
# David Degras "Regime-switching state-space models with applicationsto brain imaging"

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Description

State-space models (SSMs) with regime switching can efficiently identify recurring patterns of

variation and recurring dynamics in nonstationary multivariate time series. These models have

been successfully applied in various fields such as econometrics, signal processing, control

engineering, and object tracking. In this work we focus on the implementation of switching

SSMs in high dimension via the Expectation-Maximization (EM) algorithm. The EM algorithm

provides a relatively simple way to compute the maximum likelihood estimator (MLE) of the

model parameters. However, in switching SSMs, exact calculations are intractable as they grow

exponentially with the time series length. Even approximate calculations are burdensome with

high dimensional data. In addition, the EM algorithm has a tendency to get stuck in non-optimal

stationary points of the likelihood function, a tendency further compounded in high-dimension.

Considering two common switching SSMs, one with switching dynamics and the other with

switching observation process, we make several practical contributions: 1) we propose novel

robust initialization methods for the EM algorithm, 2) we develop a parametric bootstrap

procedure for statistical inference, 3) we provide an efficient implementation of the EM

algorithm for all discussed models in a comprehensive MATLAB package publicly available at

https://github.com/ddegras/switch-ssm. These contributions make it possible to reliably

calculate the MLE in a reasonable time, even with very long and/or high-dimensional time

series. We evaluate the statistical performance of the MLE in a simulation study and compare it

to a popular alternative approach (sliding windows correlation followed by k-means clustering).

We also present applications to the study of dynamic functional connectivity in large

electroencephalography (EEG) datasets.