Spectral Filtering for General Linear Dynamical Systems
This work addresses a fundamental challenge in control theory and machine learning for modeling complex systems, representing a significant advancement over prior methods limited to symmetric matrices.
The authors tackled the problem of learning latent-state linear dynamical systems without system identification or spectral radius assumptions, achieving a polynomial-time algorithm that extends spectral filtering to general systems with a novel convex relaxation for phase identification.
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix. The algorithm extends the recently introduced technique of spectral filtering, previously applied only to systems with a symmetric transition matrix, using a novel convex relaxation to allow for the efficient identification of phases.