Spectral Filtering for General Linear Dynamical Systems

TL;DR

This paper introduces a polynomial-time spectral filtering algorithm for learning latent-state linear dynamical systems without requiring spectral radius assumptions, extending previous methods to more general systems.

Contribution

It develops a new convex relaxation technique that enables spectral filtering to be applied to systems with non-symmetric transition matrices, broadening its applicability.

Findings

Efficient learning of general linear dynamical systems without spectral radius constraints.

Extension of spectral filtering to non-symmetric systems through convex relaxation.

Polynomial-time algorithm with theoretical guarantees.

Abstract

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.