Sparse model from optimal nonuniform embedding of time series

TL;DR

This paper introduces a method to derive sparse polynomial models from time series data using optimal nonuniform embedding, recursive optimization, and regularized least squares, demonstrated on the Mackey-Glass system.

Contribution

It presents a novel approach combining optimal nonuniform embedding with sparse polynomial modeling and efficient structure selection for time series analysis.

Findings

Effective modeling of Mackey-Glass system demonstrated

Reduces false nearest neighbors in state space reconstruction

Efficient sparse model selection via stagewise algorithm

Abstract

An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective functional that eliminates maximum number of false nearest neighbors between successive state space reconstruction cycles. A polynomial basis is then constructed from this time delay kernel. A sparse model from this polynomial basis is obtained by solving a regularized least squares problem. The constraint satisfaction problem is made computationally tractable by keeping the ratio between number of constraints to number of variable small by using fewer samples spanning all regions of the reconstructed state space. This helps the structure selection process from an exponentially large combinatorial search space. A forward stagewise algorithm is then used for fast discovery of the optimization path. Results are presented for Mackey-Glass system.