## Change Point Problems in Linear Dynamical Systems

** Onno Zoeter, Tom Heskes**; 6(Dec):1999--2026, 2005.

### Abstract

We study the problem of learning two regimes (we have a normal and a
prefault regime in mind) based on a train set of non-Markovian
observation sequences. Key to the
model is that we assume that once the system switches from the normal
to the prefault regime it cannot restore and will eventually result in
a fault. We refer to the particular setting as
*semi-supervised* since we assume the only information given
to the learner is whether a particular sequence ended with a stop
(implying that the sequence was generated by the normal regime) or
with a fault (implying that there was a switch from the normal to the
fault regime). In the latter case the particular time point at which a
switch occurred is not known.

The underlying model used is a *switching linear
dynamical system (SLDS)*. The constraints in the regime transition
probabilities result in an exact inference procedure that scales
quadratically with the length of a sequence.
Maximum aposteriori (MAP) parameter estimates can be
found using an expectation maximization (EM)
algorithm with this inference algorithm in the E-step.
For long sequences this will not be practically feasible and an
approximate inference and an approximate EM procedure is called
for. We describe a flexible class of approximations corresponding to
different choices of clusters in a Kikuchi free energy with weak
consistency constraints.

[abs][pdf]