  We address the issue of detecting changes of models that lie behind a data
stream. The model refers to an integer-valued structural information such as
the number of free parameters in a parametric model. Specifically we are
concerned with the problem of how we can detect signs of model changes earlier
than they are actualized. To this end, we employ {\em continuous model
selection} on the basis of the notion of {\em descriptive
dimensionality}~(Ddim). It is a real-valued model dimensionality, which is
designed for quantifying the model dimensionality in the model transition
period. Continuous model selection is to determine the real-valued model
dimensionality in terms of Ddim from a given data. We propose a novel
methodology for detecting signs of model changes by tracking the rise-up of
Ddim in a data stream. We apply this methodology to detecting signs of changes
of the number of clusters in a Gaussian mixture model and those of the order in
an auto regression model. With synthetic and real data sets, we empirically
demonstrate its effectiveness by showing that it is able to visualize well how
rapidly model dimensionality moves in the transition period and to raise early
warning signals of model changes earlier than they are detected with existing
methods.
