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Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target.
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Terry Lyons and Zhongmin Qian, System control and rough path , Claredon Press, 2002
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by same author, Universal kernels on non-standard input spaces , Advances in neural information processing systems, 2010, pp. 406–414
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Ben Hambly and Terry Lyons, Uniqueness for the signature of a path of bounded variation and the reduced path group , Ann. of Math. (2010), 109–167
2010
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M. Bernhart, P. Tankov, and X. Warin, A finite–dimensional approximation for pricing moving average options , SIAM Journal on Financial Mathematics 2
2011
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Terry Lyons, Rough paths, signatures and the modelling of functions on streams , Proceedings of the International Congress of Mathematicians, Korea (2014), 1–24
2014
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2018
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Sebastian Becker, Patrick Cheridito, and Arnulf Jentzen, Deep optimal stopping , Journal of Machine Learning Research 20
Junhyung Park and Krikamol Muandet, A measure-theoretic approach to kernel conditional mean embeddings , Advances in Neural Information Processing Systems 33
2020
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2021
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T. Cass, T. Lyons, and X. Xu, General signature kernels , Preprint, arXiv:2107.00447 (2021), 1–41
2021
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2021
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Bernard Lapeyre and Jérôme Lelong, Neural network regression for bermudan option pricing , Monte Carlo Methods and Applications 27
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2019
Cited alongside, same era.
M. Eder, Compactness in adapted weak topologies , Preprint, arXiv:1905.00856 (2019), 1–14
2019
Cited alongside, same era.
Patrick Kidger, Patric Bonnier, Imanol Perez Arribas, Cristopher Salvi, and Terry Lyons, Deep signature transforms , Advances in Neural Information Processing Systems 32
2019
Cited alongside, same era.
Imanol Perez Arribas, Cristopher Salvi, and Lukasz Szpruch, Sig-SDEs model for quantitative finance , Proceedings of the First ACM International Conference on AI in Finance, 2020, pp. 1–8
2020
Cited alongside, same era.
E. Bayraktar, L. Dolinski, and Y. Dolinsky, Extended weak convergence and utility maximisation with proportional transaction costs , Finance Stoch. 24
2020
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Julio Backhoff-Veraguas, Daniel Bartl, Mathias Beiglböck, and Manu Eder, Adapted Wasserstein distances and stability in mathematical finance , Finance Stoch. 24
2020
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by same author, All adapted topologies are equal , Probability Theory and Related Fields 178
2020
Cited alongside, same era.
Julio Backhoff-Veraguas, Mathias Beiglböck, Manu Eder, and Alois Pichler, Fundamental properties of process distances , Stoch. Process. Appl. (2020), 5575–5591
2020
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2021
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Maud Lemercier, Cristopher Salvi, Thomas Cass, Edwin V Bonilla, Theodoros Damoulas, and Terry J Lyons, Siggpde: Scaling sparse gaussian processes on sequential data , International Conference on Machine Learning, PMLR, 2021, pp. 6233–6242
2021
Later among the works it cites.
Maud Lemercier, Cristopher Salvi, Theodoros Damoulas, Edwin Bonilla, and Terry Lyons, Distribution regression for sequential data , International Conference on Artificial Intelligence and Statistics, PMLR, 2021, pp. 3754–3762
2021
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2021
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Cristopher Salvi, Maud Lemercier, Chong Liu, Blanka Horvath, Theo Damoulas, and Terry Lyons, Higher order kernel mean embeddings to capture filtrations of stochastic processes , Advances in Neural Information Processing Systems (2021), 1–23
2021
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Patric Bonnier, Chong Liu, and Harald Oberhauser, Adapted topologies and higher rank signatures , to appear in Ann. Appl. Probab. (2022), 1–39
2022
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Ilya Chevyrev and Harald Oberhauser, Signature moments to characterize laws of stochastic processes , Journal of Machine Learning Research (2022), 1–42
2022
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2022
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C. Bayer, H. Hager, S. Riedel, and J. Schoenmakers, Optimal stopping with signatures , Ann. Appl. Probab. (2023), 238–273
2023
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