An exemplar-based hidden Markov model framework for nonlinear state-space models

In this work we present a data-driven method for the reconstruction of dynamical systems from noisy and incomplete observation sequences. The key idea is to benefit from the availability of representative datasets of trajectories of the system of interest. These datasets provide an implicit representation of the dynamics of this system, in contrast to the explicit knowledge of the dynamical model. This data-driven strategy is of particular interest in a large variety of situations, e.g., modeling uncertainties and inconsistencies, unknown explicit models, computationally demanding models, etc. We address this exemplar-based reconstruction issue using a Hidden Markov Model (HMM) and we illustrate the relevance of the method for missing data interpolation issues in multivariate time series. As such, our contribution opens new research avenues for a variety of application domains to exploit the wealth of archived observation and simulation data, aiming a better analysis and reconstruction of dynamical systems using past and future observation sequences.