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K.-T. Chen
1954
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K.-T. Chen
1957
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1966
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1993
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T. Lyons, M. Caruana, and T. Lévy
2004
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2010
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2010
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B. Hambly and T. Lyons
2010
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T. Lyons
2014
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H. Boedihardjo, X. Geng, T. Lyons, and D. Yang
2016
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T. J. Lyons and W. Xu
2017
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T. J. Lyons and W. Xu
2018
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J. Reizenstein and B. Graham
Original
2018
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2024

Sparse Signature Coefficient Recovery via Kernels

Shmelev, Daniil, Salvi, Cristopher

Understand

Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path.

The signature poses an effective way to capture sequentially ordered information, thanks both to its rich analytic and algebraic properties as well as its universality when used as a basis to approximate functions on path space.
Whilst a truncated version of the signature can be efficiently computed using Chen's identity, there is a lack of efficient methods for computing a sparse collection of iterated integrals contained in high levels of the signature.
We address this problem by leveraging signature kernels, defined as the inner product of two signatures, and computable efficiently by means of PDE-based methods.

Built on

K.-T. Chen
1954
Earlier work this paper cites.
K.-T. Chen
1957
Earlier work this paper cites.
J. T. Day
1966
Earlier work this paper cites.
A.-M. Wazwaz
1993
Earlier work this paper cites.
T. Lyons, M. Caruana, and T. Lévy
2004
Earlier work this paper cites.
T. L. et al
2010
Earlier work this paper cites.
P. K. Friz and N. B. Victoir
2010
Earlier work this paper cites.
B. Hambly and T. Lyons
2010
Earlier work this paper cites.
T. Lyons
2014
Earlier work this paper cites.
H. Boedihardjo, X. Geng, T. Lyons, and D. Yang
2016
Earlier work this paper cites.
T. J. Lyons and W. Xu
2017
Earlier work this paper cites.
T. J. Lyons and W. Xu
2018
Earlier work this paper cites.
J. Reizenstein and B. Graham
Original
2018
Earlier work this paper cites.

Similar

J. Chang and T. Lyons
Original
2019
Cited alongside, same era.
P. Kidger, P. Bonnier, I. Perez Arribas, C. Salvi, and T. Lyons
2019
Cited alongside, same era.
F. J. Király and H. Oberhauser
2019
Cited alongside, same era.
I. P. Arribas, C. Salvi, and L. Szpruch
2020
Cited alongside, same era.
P. Kidger and T. Lyons
Original
2020
Cited alongside, same era.
P. Kidger and T. Lyons
Original
2020
Cited alongside, same era.