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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
78/2018

Learning Paths from Signature Tensors

Max Pfeffer, Anna Seigal and Bernd Sturmfels

Abstract

Matrix congruence extends naturally to the setting of tensors. We apply methods from tensor decomposition, algebraic geometry and numerical optimization to this group action. Given a tensor in the orbit of another tensor, we compute a matrix which transforms one to the other. Our primary application is an inverse problem from stochastic analysis: the recovery of paths from their signature tensors of order three. We establish identifiability results and recovery algorithms for piecewise linear paths, polynomial paths, and generic dictionaries. A detailed analysis of the relevant condition numbers is presented. We also compute the shortest path with a given signature tensor.

Received:
Sep 10, 2018
Published:
Sep 10, 2018

Related publications

inJournal
2019 Repository Open Access
Max Pfeffer, Anna Seigal and Bernd Sturmfels

Learning paths from signature tensors

In: SIAM journal on matrix analysis and applications, 40 (2019) 2, pp. 394-416