Detecting Signs of Model Change with Continuous Model Selection Based on Descriptive Dimensionality

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.