Chaotic billiard dynamics for herding

抄録

Herding systems are discrete-time nonlinear dynamical systems designed efficiently for statistical inference. In this paper, we introduce a continuous-time version of these systems, which we call herding billiard systems. In contrast to the weakly chaotic dynamics of the original version, the continuous-time version is shown to have chaotic pseudo-billiard dynamics, while inheriting the fundamental sampling functions. We also present the connection between these two versions. Thus, herding billiard systems provide a novel approach to the complexity of herding systems from the viewpoint of chaotic billiard dynamics.