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These notes expound the recent use of the signature transform and rough path theory in data science and machine learning.
A Course in Mathematical Analysis: pt. 2. Differential equations.[c1917
Edouard Goursat · 1916
Earlier work this paper cites.
The radiation theories of tomonaga, schwinger, and feynman
Freeman J Dyson · 1949
Earlier work this paper cites.
Theory of reproducing kernels
Nachman Aronszajn · 1950
Earlier work this paper cites.
Iterated integrals and exponential homomorphisms
Kuo-Tsai Chen · 1954
Earlier work this paper cites.
On the exponential solution of differential equations for a linear operator
Wilhelm Magnus · 1954
Earlier work this paper cites.
Integration of paths, geometric invariants and a generalized baker-hausdorff formula
Kuo-Tsai Chen · 1957
Earlier work this paper cites.
The goursat problem
Milton Lees · 1960
Earlier work this paper cites.
Formal differential equations
Kuo-tsai Chen · 1961
Earlier work this paper cites.
A runge-kutta method for the numerical solution of the goursat problem in hyperbolic partial differential equations
J. T. Day · 1966
Earlier work this paper cites.
An algebraic approach to nonlinear functional expansions
Michel Fliess, Moustanir Lamnabhi, and Françoise Lamnabhi-Lagarrigue · 1983
Earlier work this paper cites.
On the numerical solution for the goursat problem
A. M. Wazwaz · 1993
Earlier work this paper cites.
Variable step size control in the numerical solution of stochastic differential equations
Jessica G Gaines and Terry J Lyons · 1997
Earlier work this paper cites.
Noncommutative power series and formal lie-algebraic techniques in nonlinear control theory
Matthias Kawski and Héctor J Sussmann · 1997
Earlier work this paper cites.
Differential equations driven by rough signals
Terry J Lyons · 1998
Earlier work this paper cites.
Real analysis: modern techniques and their applications
Gerald B Folland · 1999
Earlier work this paper cites.
Approximation theory of the mlp model in neural networks
Allan Pinkus · 1999
Earlier work this paper cites.
A modern course in statistical physics, 1999
Linda E Reichl · 1999
Earlier work this paper cites.
Collected Papers of KT Chen
Kuo-Tsai Chen and Philippe Tondeur · 2001
Earlier work this paper cites.
The spectrum kernel: A string kernel for svm protein classification
Christina Leslie, Eleazar Eskin, and William Stafford Noble · 2001
Earlier work this paper cites.
A generalized representer theorem
Bernhard Schölkopf, Ralf Herbrich, and Alex J Smola · 2001
Earlier work this paper cites.
Problems in stochastic analysis: Connections between rough paths and non-commutative harmonic analysis
Thomas Fawcett · 2002
Earlier work this paper cites.
Text classification using string kernels
Huma Lodhi, Craig Saunders, John Shawe-Taylor, Nello Cristianini, and Chris Watkins · 2002
Earlier work this paper cites.
Free Lie algebras
Christophe Reutenauer · 2003
Earlier work this paper cites.
An introduction to numerical analysis
Endre Süli and David F Mayers · 2003
Earlier work this paper cites.
Controlling rough paths
Massimiliano Gubinelli · 2004
Earlier work this paper cites.
Kernel methods in computational biology
Bernhard Schölkopf, Koji Tsuda, Jean-Philippe Vert, et al · 2004
Earlier work this paper cites.
What is a support vector machine?
William S Noble · 2006
Earlier work this paper cites.
Measure theory
Vladimir Igorevich Bogachev and Maria Aparecida Soares Ruas · 2007
Earlier work this paper cites.
A kernel for time series based on global alignments
Marco Cuturi, Jean-Philippe Vert, Oystein Birkenes, and Tomoko Matsui · 2007
Earlier work this paper cites.
Differential equations driven by rough paths: an approach via discrete approximation
Alexander M Davie · 2007
Earlier work this paper cites.
A kernel statistical test of independence
Arthur Gretton, Kenji Fukumizu, Choon Teo, Le Song, Bernhard Schölkopf, and Alex Smola · 2007
Earlier work this paper cites.
Differential equations driven by rough paths
Terry J Lyons, Michael Caruana, and Thierry Lévy · 2007
Earlier work this paper cites.
A hilbert space embedding for distributions
Alex Smola, Arthur Gretton, Le Song, and Bernhard Schölkopf · 2007
Cited alongside, same era.
Numerical methods for approximating solutions to rough differential equations
Lajos Gergely Gyurkó · 2008
Cited alongside, same era.
Universal kernels on non-standard input spaces
Andreas Christmann and Ingo Steinwart · 2010
Cited alongside, same era.
Coropa computational rough paths (software library)
Terry Lyons et al · 2010
Cited alongside, same era.
Multidimensional stochastic processes as rough paths: theory and applications
Peter K Friz and Nicolas B Victoir · 2010
Cited alongside, same era.
Rough paths based numerical algorithms in computational finance
Lajos Gergely Gyurkó and Terry Lyons · 2010
Cited alongside, same era.
A course on rough paths
Peter K Friz and Martin Hairer · 2020
Later among the works it cites.
Patrick Kidger and Terry Lyons · 2020
Later among the works it cites.
Universal approximation with deep narrow networks
Patrick Kidger and Terry Lyons · 2020
Later among the works it cites.
Neural controlled differential equations for irregular time series
Patrick Kidger, James Morrill, James Foster, and Terry Lyons · 2020
Later among the works it cites.
Metrizing weak convergence with maximum mean discrepancies
Carl-Johann Simon-Gabriel, Alessandro Barp, Bernhard Schölkopf, and Lester Mackey · 2020
Later among the works it cites.
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Uniqueness for the signature of a path of bounded variation and the reduced path group
Ben Hambly and Terry Lyons · 2010
Cited alongside, same era.
Hilbert space embeddings and metrics on probability measures
Bharath K Sriperumbudur, Arthur Gretton, Kenji Fukumizu, Bernhard Schölkopf, and Gert RG Lanckriet · 2010
Cited alongside, same era.
A kernel two-sample test
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
Cited alongside, same era.
Order book models, signatures and numerical approximations of rough differential equations
Arend Janssen · 2012
Cited alongside, same era.
Learning from distributions via support measure machines
Krikamol Muandet, Kenji Fukumizu, Francesco Dinuzzo, and Bernhard Schölkopf · 2012
Cited alongside, same era.
Kernel-based conditional independence test and application in causal discovery
Kun Zhang, Jonas Peters, Dominik Janzing, and Bernhard Schölkopf · 2012
Cited alongside, same era.
Bayesian learning from sequential data using gaussian processes with signature covariances
Csaba Toth and Harald Oberhauser · 2020
Later among the works it cites.
Sk-tree: a systematic malware detection algorithm on streaming trees via the signature kernel
Thomas Cochrane, Peter Foster, Varun Chhabra, Maud Lemercier, Cristopher Salvi, and Terry Lyons · 2021
Later among the works it cites.
Neural sdes as infinite-dimensional gans
Patrick Kidger, James Foster, Xuechen Li, Harald Oberhauser, and Terry Lyons · 2021
Later among the works it cites.
Siggpde: Scaling sparse gaussian processes on sequential data
Maud Lemercier, Cristopher Salvi, Thomas Cass, Edwin V Bonilla, Theodoros Damoulas, and Terry Lyons · 2021
Later among the works it cites.
Distribution regression for sequential data
Maud Lemercier, Cristopher Salvi, Theodoros Damoulas, Edwin Bonilla, and Terry Lyons · 2021
Later among the works it cites.
Neural rough differential equations for long time series
James Morrill, Cristopher Salvi, Patrick Kidger, and James Foster · 2021
Later among the works it cites.
The signature kernel is the solution of a goursat pde
Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons, and Weixin Yang · 2021
Later among the works it cites.
Higher order kernel mean embeddings to capture filtrations of stochastic processes
Cristopher Salvi, Maud Lemercier, Chong Liu, Blanka Hovarth, Theodoros Damoulas, and Terry Lyons · 2021
Later among the works it cites.
Signature moments to characterize laws of stochastic processes
Ilya Chevyrev and Harald Oberhauser · 2022
Later among the works it cites.
On neural differential equations
Patrick Kidger · 2022
Later among the works it cites.
Runge-kutta methods for rough differential equations
Martin Redmann and Sebastian Riedel · 2022
Later among the works it cites.
Neural stochastic pdes: Resolution-invariant learning of continuous spatiotemporal dynamics
Cristopher Salvi, Maud Lemercier, and Andris Gerasimovics · 2022
Later among the works it cites.
Signature asymptotics, empirical processes, and optimal transport
Thomas Cass, Remy Messadene, and William F Turner · 2023
Later among the works it cites.
A fubini type theorem for rough integration
Thomas Cass and Jeffrey Pei · 2023
Later among the works it cites.
Neural signature kernels as infinite-width-depth-limits of controlled resnets
Nicola Muca Cirone, Maud Lemercier, and Cristopher Salvi · 2023
Later among the works it cites.
Global universal approximation of functional input maps on weighted spaces
Christa Cuchiero, Philipp Schmocker, and Josef Teichmann · 2023
Later among the works it cites.
New directions in the applications of rough path theory
Adeline Fermanian, Terry Lyons, James Morrill, and Cristopher Salvi · 2023
Later among the works it cites.
A neural rde approach for continuous-time non-markovian stochastic control problems
Melker Hoglund, Emilio Ferrucci, Camilo Hernandez, Aitor Muguruza Gonzalez, Cristopher Salvi, Leandro Sanchez-Betancourt, and Yufei Zhang · 2023
Later among the works it cites.
Optimal stopping via distribution regression: a higher rank signature approach
Blanka Horvath, Maud Lemercier, Chong Liu, Terry Lyons, and Cristopher Salvi · 2023
Later among the works it cites.
A structure theorem for streamed information
Cristopher Salvi, Joscha Diehl, Terry Lyons, Rosa Preiss, and Jeremy Reizenstein · 2023
Later among the works it cites.
On the wiener chaos expansion of the signature of a gaussian process
Thomas Cass and Emilio Ferrucci · 2024
Closest in time.
Weighted signature kernels
Thomas Cass, Terry Lyons, and Xingcheng Xu · 2024
Closest in time.
Free probability, path developments and signature kernels as universal scaling limits
Thomas Cass and William F Turner · 2024
Closest in time.
Topologies on unparameterised path space
Thomas Cass and William F Turner · 2024
Closest in time.
Non-adversarial training of neural sdes with signature kernel scores
Zacharia Issa, Blanka Horvath, Maud Lemercier, and Cristopher Salvi · 2024
Closest in time.
Signature kernel conditional independence tests in causal discovery for stochastic processes
Georg Manten, Cecilia Casolo, Emilio Ferrucci, Søren Wengel Mogensen, Cristopher Salvi, and Niki Kilbertus · 2024
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A path-dependent pde solver based on signature kernels
Alexandre Pannier and Cristopher Salvi · 2024
Closest in time.