Compressible reparametrization of time-variant linear dynamical systems

Abstract

Linear dynamical systems (LDS) are applied to model data from various domains-including physics, smart cities, medicine, biology, chemistry and social science-as stochastic dynamic process. Whenever the model dynamics are allowed to change over time, the number of parameters can easily exceed millions. Hence, an estimation of such time-variant dynamics on a relatively small-compared to the number of variables-training sample typically results in dense, overfitted models. Existing regularization techniques are not able to exploit the temporal structure in the model parameters. We investigate a combined reparametrization and regularization approach which is designed to detect redundancies in the dynamics in order to leverage a new level of sparsity. On the basis of ordinary linear dynamical systems, the new model, called ST-LDS, is derived and a proximal parameter optimization procedure is presented. Differences to l1-regularization-based approaches are discussed and an evaluation on synthetic data is conducted. The results show, that the larger the considered system, the more sparsity can be achieved, compared to plain l1-regularization.