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The Insertion Method to Invert the Signature of a Path

In: Recent Advances in Econometrics and Statistics

Author

Listed:
  • Adeline Fermanian

    (Califrais’ Machine Learning Lab, LOPF)

  • Jiawei Chang

    (University of Oxford, Department of Mathematics)

  • Terry Lyons

    (University of Oxford, The Alan Turing Institute, Department of Mathematics)

  • Gérard Biau

    (Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, CNRS)

Abstract

The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation and reparameterization. Therefore, a crucial question of interest is the development of efficient algorithms to invert the signature, i.e., to reconstruct the path from the information of its (truncated) signature. In this article, we study the insertion procedure, originally introduced by Chang and Lyons (Insertion algorithm for inverting the signature of a path, 2019. arXiv:1907.08423), from both a theoretical and a practical point of view. After describing our version of the method, we give its rate of convergence for piecewise linear paths, accompanied by an implementation in PyTorch. The algorithm is parallelized, meaning that it is very efficient at inverting a batch of signatures simultaneously. Its performance is illustrated with both real-world and simulated examples.

Suggested Citation

  • Adeline Fermanian & Jiawei Chang & Terry Lyons & Gérard Biau, 2024. "The Insertion Method to Invert the Signature of a Path," Springer Books, in: Matteo Barigozzi & Siegfried Hörmann & Davy Paindaveine (ed.), Recent Advances in Econometrics and Statistics, pages 575-595, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61853-6_29
    DOI: 10.1007/978-3-031-61853-6_29
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