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Abstract:
We describe an ecient variational Bayesian approximation scheme for model structure selec- tion in Linear Gaussian State-Space based Models (LGSSMs) (also known as Linear Dynamical Systems), which include LGSSMs, mixtures of LGSSMs and switching LGSSMs. In a Bayesian approach the model parameters are considered as random variables and inte- grated out yielding the marginal likelihood of the data. By using appropriate parameter prior distributions, we enforce a sparse parametrization, i.e. we bias the model to select the smallest set of parameters that explains the data well. This enables us to perform model structure se- lection, i.e. to determine an appropriate number of hidden variables, mixture components and switching variables, based on the Occams razor principle. In contrast to other approaches, such as Bayesian Information Criterion-based approaches which need to train a separate model for each possible model structure, in our approach the selection is performed within a single model. This way the computational overhead of training a large number of models with dierent struc- tures is avoided. The model specication and subsequent inference and training pose some considerable chal- lenges due to intractability issues. We describe how these may be addressed using a variational approximation, in which the problem is formulated such that ecient inference methods can be used. As an application example, we show that our approach can be used to identify dynami- cally similar segments of motions underlying multidimensional time-series generated from hu- man video recordings, without using any prior knowledge on the number of segment-types and segment boundaries.
