# Functional linear regression with truncated signatures

arXiv: https://arxiv.org/abs/2006.08442 · HTML: https://mlsanity.com/paper/2006.08442/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 6 of 6)

- [scikit-fda: A Python Package for Functional Data Analysis](https://mlsanity.com/paper/2211.02566/) (2022)
- [The Signature Kernel](https://mlsanity.com/paper/2305.04625/) (2023)
- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)
- [Learning the Dynamics of Sparsely Observed Interacting Systems](https://mlsanity.com/paper/2301.11647/) (2023)
- [Sliding-Window Signatures for Time Series: Application to Electricity Demand Forecasting](https://mlsanity.com/paper/2510.12337/) (2025)
- [Local regression on path spaces with signature metrics](https://mlsanity.com/paper/2510.16728/) (2025)

## Abstract (arXiv)

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.