Learning Paths from Signature Tensors
| Autor: | Max Pfeffer, Anna Seigal, Bernd Sturmfels |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
FOS: Computer and information sciences
Computer Science - Machine Learning MathematicsofComputing_NUMERICALANALYSIS Mathematics - Statistics Theory Statistics Theory (math.ST) 010103 numerical & computational mathematics Algebraic geometry 01 natural sciences Machine Learning (cs.LG) Mathematics - Algebraic Geometry Matrix congruence ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION FOS: Mathematics Tensor Mathematics - Numerical Analysis 0101 mathematics Algebraic Geometry (math.AG) Mathematics ComputingMethodologies_COMPUTERGRAPHICS Group (mathematics) Numerical Analysis (math.NA) Inverse problem Action (physics) Algebra Identifiability Signature (topology) Analysis 14Q15 15A72 65K10 |
| Popis: | 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 third order signature tensors. We establish identifiability results, both exact and numerical, for piecewise linear paths, polynomial paths, and generic dictionaries. Numerical optimization is applied for recovery from inexact data. We also compute the shortest path with a given signature tensor. 22 pages, 3 figures |
| Databáze: | OpenAIRE |
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