Learning Paths from Signature Tensors

DOI10.1137/18M1212331zbMath1469.14116arXiv1809.01588OpenAlexW2890252560WikidataQ114074290 ScholiaQ114074290MaRDI QIDQ4631266

Max Pfeffer, Bernd Sturmfels, Anna Leah Seigal

Publication date: 24 April 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.01588

zbMATH Keywords

optimizationinverse problemsidentifiabilitytensor decompositionsignature tensorscongruence action

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Vector and tensor algebra, theory of invariants (15A72) Computational aspects of higher-dimensional varieties (14Q15)

Related Items (7)

On the Complexity of Isomorphism Problems for Tensors, Groups, and Polynomials I: Tensor Isomorphism-Completeness ⋮ Developing the Path Signature Methodology and Its Application to Landmark- Based Human Action Recognition ⋮ Smooth rough paths, their geometry and algebraic renormalization ⋮ Signatures of paths transformed by polynomial maps ⋮ Toric geometry of path signature varieties ⋮ A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula ⋮ The rough Veronese variety

Uses Software

• Macaulay2
• Manopt
• Tensorlab
• signature-invariants

Cites Work

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• Tensor Decompositions and Applications
• Hyperbolic development and inversion of signature
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• Inverting the signature of a path
• Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number
• Generically free representations. II: Irreducible representations
• The rough Veronese variety
• Invariants of multidimensional time series based on their iterated-integral signature
• Stationary subgroups of points of general position in the representation space of a semisimple Lie group
• Condition
• Manopt, a Matlab toolbox for optimization on manifolds
• Relative bilinear complexity and matrix multiplication.
• VARIETIES OF SIGNATURE TENSORS
• System Control and Rough Paths
• Incorporating Condition Measures into the Complexity Theory of Linear Programming
• Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory
• A course on rough paths. With an introduction to regularity structures
• The Euclidean distance degree of an algebraic variety

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