Variational Inference and Learning of Piecewise-linear Dynamical Systems

International audienceModeling 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

Variational Inference for 3-D Localization and Tracking of Multiple Targets Using Multiple Cameras

This paper proposes a novel unified framework to solve the 3-D localization and tracking problem that occurs multiple camera settings with overlapping views. The main challenge is to overcome the uncertainty of the back projection arising from the challenges of ground point detection in an environment that includes severe occlusions and the unknown heights of people. To tackle this challenge, we establish a Bayesian learning framework that maximizes a posterior over the trajectory assignments and 3-D positions for given detections from multiple cameras. To solve the Bayesian learning problem in a tractable form, we develop an expectation-maximization scheme based on the variation inference approximation, where the probability distributions are designed to follow Boltzmann distributions of seven terms that are induced from multicamera tracking settings. The experimental results show that the proposed method outperforms the state-of-the-art methods on the challenging multicamera data sets.N