Functional linear regression with truncated signatures

TL;DR

This paper introduces a new functional regression method using truncated signatures to effectively model high-dimensional functional covariates, supported by theoretical guarantees and empirical validation.

Contribution

It proposes a novel signature-based regression approach with truncation, providing estimators and theoretical analysis for high-dimensional functional data.

Findings

Method is competitive with traditional models

Performs well with high-dimensional covariates

Theoretical guarantees support the estimator's validity

Abstract

We place ourselves in a functional regression setting and propose a novel methodology for regressing a real output on vector-valued functional covariates. This methodology is based on the notion of signature, which is a representation of a function as an infinite series of its iterated integrals. The signature depends crucially on a truncation parameter for which an estimator is provided, together with theoretical guarantees. An empirical study on both simulated and real-world datasets shows that the resulting methodology is competitive with traditional functional linear models, in particular when the functional covariates take their values in a high dimensional space.