Predicting sparse circle maps from their dynamics

TL;DR

This paper establishes theoretical guarantees for recovering sparse circle maps from their dynamics, demonstrating near-linear sample complexity in the sparsity, which advances understanding of sparse dynamical system identification.

Contribution

It provides the first recovery guarantees for ergodic circle systems modeled by sparse trigonometric polynomials, linking sparsity and sample complexity.

Findings

Recovery guarantees scale near-linearly with sparsity

Sparse trigonometric polynomial models enable efficient system identification

Theoretical bounds improve understanding of dynamical system recovery

Abstract

The problem of identifying a dynamical system from its dynamics is of great importance for many applications. Recently it has been suggested to impose sparsity models for improved recovery performance. In this paper, we provide recovery guarantees for such a scenario. More precisely, we show that ergodic systems on the circle described by sparse trigonometric polynomials can be recovered from a number of samples scaling near-linearly in the sparsity.