Page 261 - Contributed Paper Session (CPS) - Volume 4

CPS2220 David Degras et al.
1. Introduction
Regime-switching state-space models (in short, switching SSMs) form a
powerful class of time series models used in fields as varied as econometrics
[7], speech recognition [12], computer vision [1], and tecently neuroimaging
[11]. Switching SSMs can flexibly track nonstationary behavior and identify
(possibly low-dimensional) latent factors in time series. These models are
particularly suitable in situations where dependencies between study variables
are modulated by an underlying regime of activity. In econometrics, for
example, such regimes could be “growth cycle” and “recession cycle”.
Several computational methods are available for switching SSMs. Bayesian
approaches include Gibbs sampling [8], variational Bayes [4], and sequential
Monte Carlo [3]. Frequentist approaches are typically based on the maximum
likelihood estimator (MLE) and the Expectation-Maximization (EM) algorithm
(2, 5, 7, 13]. In practice, switching SSMs have been mostly applied to low-
dimensional and telatively short time series. The case of high-dimensional
and/or long time series, which is our focus here, poses considerable numerical
challenges both for model fitting and statistical inference. Also, to our
knowledge, there are currently no publicly available software packages for
switching SSMs.
This work aims to facilitate the implementation of switching SSMs with
large datasets. We study two broadly applicable switching SSMs and their
implementation via the EM algorithm. Our contributions are as follows. First,
we provide two new initialization methods for the EM based on least square
regression, K-means clustering. and dichotomic search. Indeed, the choice of
starting points is often key to the successful convergence of optimization
algorithms, especially for large datasets and models with many parameters.
Second, we provide numerical optimization tools to handle constraints on the
model parameters such as equality constraints, fixed coefficients constraints,
or scaling constraints.
Such constraints can prove important both for model interpretability and
for numerical stability and convergence of the EM. Third, we develop a
parametric bootstrap method for the statistical inference of model
parameters. In our experience, likelihood-based inference is not tractable in
high-dimensional switching SSMs: the proposed bootstrap offers a viable
alternative that can easily be computed in parallel. Fourth, we implement our
approach in a suite of MATLAB functions available at
https://github.com/ddegras/svitch-ssa. Applications of our switching SSMs to
large electro-encephalography (EEG) data from an epilepsy study and a brain
computer interface study will be presented orally (but not here for reasons of
space).
The paper is organized as follows. Section 2 gives a general account of
switching SSMs and introduces our study models. Section 3 briefly describes

250 | I S I W S C 2 0 1 9