Functional linear regression with truncated signatures

2020/06/15 by Fermanian, Adeline · 6 citations
#60L10 (Secondary) #62R10 (Primary) #FOS: Computer and information sciences #Methodology (stat.ME)

paper · doi:10.48550/arxiv.2006.08442

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.

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