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SUMMARY:David Degras "Regime-switching state-space models with application
sto brain imaging"
DTSTART;VALUE=DATE-TIME:20190612T083000Z
DTEND;VALUE=DATE-TIME:20190612T093000Z
DTSTAMP;VALUE=DATE-TIME:20191209T102021Z
UID:indico-event-4593@indico.math.cnrs.fr
DESCRIPTION:State-space models (SSMs) with regime switching can efficientl
y identify recurring patterns of\nvariation and recurring dynamics in nons
tationary multivariate time series. These models have\nbeen successfully a
pplied in various fields such as econometrics\, signal processing\, contro
l\nengineering\, and object tracking. In this work we focus on the impleme
ntation of switching\nSSMs in high dimension via the Expectation-Maximizat
ion (EM) algorithm. The EM algorithm\nprovides a relatively simple way to
compute the maximum likelihood estimator (MLE) of the\nmodel parameters. H
owever\, in switching SSMs\, exact calculations are intractable as they gr
ow\nexponentially with the time series length. Even approximate calculatio
ns are burdensome with\nhigh dimensional data. In addition\, the EM algori
thm has a tendency to get stuck in non-optimal\nstationary points of the l
ikelihood function\, a tendency further compounded in high-dimension.\nCon
sidering two common switching SSMs\, one with switching dynamics and the o
ther with\nswitching observation process\, we make several practical contr
ibutions: 1) we propose novel\nrobust initialization methods for the EM al
gorithm\, 2) we develop a parametric bootstrap\nprocedure for statistical
inference\, 3) we provide an efficient implementation of the EM\nalgorithm
for all discussed models in a comprehensive MATLAB package publicly avail
able at\nhttps://github.com/ddegras/switch-ssm. These contributions make i
t possible to reliably\ncalculate the MLE in a reasonable time\, even with
very long and/or high-dimensional time\nseries. We evaluate the statistic
al performance of the MLE in a simulation study and compare it\nto a popul
ar alternative approach (sliding windows correlation followed by k-means c
lustering).\nWe also present applications to the study of dynamic function
al connectivity in large\nelectroencephalography (EEG) datasets.\n\nhttps:
//indico.math.cnrs.fr/event/4593/
LOCATION:318
URL:https://indico.math.cnrs.fr/event/4593/
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