Spectral learning of dynamic systems from nonequilibrium data
This enables modeling of large-time scale systems without requiring identically distributed data, which is incremental but addresses a specific bottleneck in spectral learning.
The paper tackles the problem of learning dynamic systems from nonequilibrium data, showing that equilibrium dynamics can be extracted by imposing an equilibrium constraint, and proposes a binless extension for continuous data with linear complexity.
Observable operator models (OOMs) and related models are one of the most important and powerful tools for modeling and analyzing stochastic systems. They exactly describe dynamics of finite-rank systems and can be efficiently and consistently estimated through spectral learning under the assumption of identically distributed data. In this paper, we investigate the properties of spectral learning without this assumption due to the requirements of analyzing large-time scale systems, and show that the equilibrium dynamics of a system can be extracted from nonequilibrium observation data by imposing an equilibrium constraint. In addition, we propose a binless extension of spectral learning for continuous data. In comparison with the other continuous-valued spectral algorithms, the binless algorithm can achieve consistent estimation of equilibrium dynamics with only linear complexity.