Learning sequential data with the help of linear systems

The aim of the paper is to show that linear dynamical systems can be quite useful when dealing with sequence learning tasks. According to the complexity of the problem to face, linear dynamical systems may directly contribute to provide a good solution at a reduced computational cost, or indirectly provide support at a pre-training stage for nonlinear models. We present and discuss several approaches, both linear and nonlinear, where linear dynamical systems play an important role. These approaches are empirically assessed on two nontrivial datasets of sequences on a prediction task. Experimental results show that indeed linear dynamical systems can either directly provide a satisfactory solution, as well as they may be crucial for the success of more sophisticated nonlinear approaches.