Variational Inference and Learning of Piecewise Linear Dynamical Systems

Area of Science:

• Dynamical Systems Modeling
• Machine Learning
• Signal Processing

Background:

• Accurate modeling of temporal data is crucial across scientific and engineering disciplines.
• Traditional linear-Gaussian models are insufficient for processes with multiple behavioral modes.
• Switching dynamical systems offer flexibility but face computational intractability due to exponential complexity.

Purpose of the Study:

• To develop a computationally tractable variational approximation for piecewise linear dynamical systems.
• To introduce efficient variational expectation-maximization (EM) algorithms for filtering and smoothing.
• To enable offline estimation of static model parameters and the number of linear modes.

Main Methods:

• Proposed a variational approximation for piecewise linear dynamical systems.
• Derived two variational EM algorithms: a filter and a smoother.
• Demonstrated parameter splitting into static and dynamic sets for offline estimation.

Main Results:

• The proposed variational approximation effectively handles piecewise linear dynamics.
• Static parameters and the number of modes can be estimated offline.
• The method was successfully applied to head-pose tracking, showing competitive performance.

Conclusions:

• The variational approximation offers an efficient solution for modeling complex, multi-modal temporal data.
• The developed algorithms provide a robust framework for parameter estimation and state inference.
• This approach advances the state-of-the-art in dynamical systems modeling and tracking applications.