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math.RA2025
An Efficient Algorithm for Path Recovery from Signature Tensors
Leonard Schmitz
We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis. Our algorithm provides the exact solution to this re…
math.RA2025
Learning Barycenters from Signature Matrices
Carlos Améndola, Leonard Schmitz
The expected signature of a family of paths need not be a signature of a path itself. Motivated by this, we consider the notion of a Lie group barycenter introduced by Buser and Ka…
math.RA2024
Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra
Leonard Schmitz, Nikolas Tapia
Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from -algebras and a novel two-pa…