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Abstract

Unsupervised time-series segmentation in the general scenario in which the number of segment-types
and segment boundaries are a priori unknown is a fundamental problem in many applications and requires an accurate segmentation model as well as a way of determining an appropriate number of segment-types.
In most approaches, segmentation and determination of number of segment-types are addressed
in two separate steps, since the segmentation model assumes a predefined number of segment-types.
The determination of number of segment-types is thus achieved by training and comparing several separate models. In this paper, we take a Bayesian approach to a segmentation model based on linear Gaussian state-space models to achieve structure selection within the model. An appropriate prior distribution on the parameters is used to enforce a sparse parametrization, such that the model automatically selects the smallest number of underlying dynamical systems that explain the data well and a parsimonious structure for each dynamical system. As the resulting model is computationally intractable, we introduce a variational approximation, in which a reformulation of the problem enables to use an efficient inference algorithm.