Page 260 - Contributed Paper Session (CPS) - Volume 4

CPS2220 David Degras et al.

Regime-switching state-space models with
applications to brain imaging
1
2
3
David Degras , Chee Ming Ting , Hernando Ombao
1 University of Massachusetts Boston
2 Universiti Teknologi Malaysia
3 King Abdullah University of Science and Technology

Abstract
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.

Keywords
Nonstationary time series, Computational statistics, High-dimensional data,
EM algorithm

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