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Variational Inference and Learning of Piecewise-linear Dynamical Systems

Xavier Alameda-Pineda 1 Vincent Drouard 1, 2 Radu Horaud 1
1 PERCEPTION - Interpretation and Modelling of Images and Videos
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many real-world processes that cannot be characterized by a single linear behavior. Alternatively, it is possible to consider a piecewise-linear model which, combined with a switching mechanism, is well suited when several modes of behavior are needed. Nevertheless, switching dynamical systems are intractable because their computational complexity increases exponentially with time. In this paper, we propose a variational approximation of piecewise linear dynamical systems. We provide full details of the derivation of two variational expectation-maximization algorithms, a filter and a smoother. We show that the model parameters can be split into two sets, static and dynamic parameters, and that the former parameters can be estimated off-line together with the number of linear modes, or the number of states of the switching variable. We apply the proposed method to a visual tracking problem, namely head-pose tracking, and we thoroughly compare our algorithms with several state of the art trackers.
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https://hal.archives-ouvertes.fr/hal-02745527
Contributor : Team Perception <>
Submitted on : Tuesday, January 26, 2021 - 2:11:52 PM
Last modification on : Monday, February 22, 2021 - 12:15:12 PM

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  • HAL Id : hal-02745527, version 3
  • ARXIV : 2006.01668

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Xavier Alameda-Pineda, Vincent Drouard, Radu Horaud. Variational Inference and Learning of Piecewise-linear Dynamical Systems. IEEE Transactions on Neural Networks and Learning Systems, IEEE, 2021. ⟨hal-02745527v3⟩

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