case. Contrary to the supervised case, no a priori information about the regimes can be
used, so only two PDFs are used: at each time step, one PDF is estimated assuming there
was no change in the data stationarity (hypothesis HO), and one assuming there was a
change at a certain time step inside the window (hypothesis HI). Then the log-likelihood
ratio of those two PDFs is monitored until it reaches a threshold, indicating a change
from HO to HI, and records the position of the change point and starts again. This
approach [9, 10], implemented by the generalized likelihood ratio (GLR) test does not
keep a memory of past regions since all information is discarded after detection of a
change point. The processes we are interested in switch between a small number of
subprocesses, therefore it seems more appropriate to consider approaches that can re-use
previously learned information. Although the GLR test is usually considered as a
benchmark to compare other segmentation algorithms to, it has a high computational
complexity, especially with non-linear predictors, and will not be used in this thesis.
2.2.3 Competitive Experts Approach
2.2.3.1 The mixture of experts
Another approach can be taken when some information about the data is known:
more specifically when the data is known to switch among a finite number P of
subprocesses, called regimes, it is indeed interesting to be able to identify a new segment
of data to an already trained expert. One obvious way to preserve the information learned
about each subprocess is to train one predictor (or expert) for each subprocess. An
application of this idea is the Mixture of Experts (MOE) model [11], where several
experts and a gate see the same input: the output is a sum weighted by the gate of the
experts' outputs, and the system attempts to model the overall PDF of the data as a