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Generative adversarial networks (GANs) have been extremely successful in generating samples, from seemingly high dimensional probability measures.
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Ioannis Karatzas and Steven E Shreve · 1998
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Problems in stochastic analysis: Connections between rough paths and non-commutative harmonic analysis
Thomas Fawcett · 2002
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On discriminative vs. generative classifiers: A comparison of logistic regression and naive bayes
Andrew Y Ng and Michael I Jordan · 2002
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A continuous-time garch process driven by a lévy process: stationarity and second-order behaviour
Claudia Klüppelberg, Alexander Lindner, and Ross Maller · 2004
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Ruey S Tsay · 2005
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Differential equations driven by rough paths
Terry J Lyons, Michael Caruana, and Thierry Lévy · 2007
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Gerd Heber, Asger Lunde, Neil Shephard, and Kevin Sheppard · 2009
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Uniqueness for the signature of a path of bounded variation and the reduced path group
B.M. Hambly and Terry Lyons · 2010
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Learning from the past, predicting the statistics for the future, learning an evolving system
Daniel Levin, Terry Lyons, and Hao Ni · 2013
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The uniqueness of signature problem in the non-markov setting
Horatio Boedihardjo and Xi Geng · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
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Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2015
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Generative moment matching networks
Yujia Li, Kevin Swersky, and Rich Zemel · 2015
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Expected signature of brownian motion up to the first exit time from a bounded domain
Terry Lyons, Hao Ni, et al · 2015
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A primer on the signature method in machine learning
Ilya Chevyrev and Andrey Kormilitzin · 2016
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Characteristic functions of measures on geometric rough paths
Ilya Chevyrev, Terry Lyons, et al · 2016
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Conditional generative moment-matching networks
Yong Ren, Jun Zhu, Jialian Li, and Yucen Luo · 2016
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Constantinos Daskalakis, Andrew Ilyas, Vasilis Syrgkanis, and Haoyang Zeng · 2017
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Real-valued (medical) time series generation with recurrent conditional gans, 2017
Cristóbal Esteban, Stephanie L. Hyland, and Gunnar Rätsch · 2017
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Improved training of wasserstein gans
Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville · 2017
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Gans trained by a two time-scale update rule converge to a local nash equilibrium
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter · 2017
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Are gans created equal? a large-scale study
Mario Lucic, Karol Kurach, Marcin Michalski, Sylvain Gelly, and Olivier Bousquet · 2017
On finding local nash equilibria (and only local nash equilibria) in zero-sum games
Eric V Mazumdar, Michael I Jordan, and S Shankar Sastry · 2019
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On the signature and cubature of the fractional brownian motion for h¿12
Riccardo Passeggeri · 2019
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Deep hedging: Learning to simulate equity option markets
Magnus Wiese, Lianjun Bai, Ben Wood, and Hans Buehler · 2019
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Time-series generative adversarial networks
Jinsung Yoon, Daniel Jarrett, and Mihaela van der Schaar · 2019
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Generating synthetic data in finance: opportunities, challenges and pitfalls
Samuel Assefa, Danial Dervovic, Mahmoud Mahfouz, Tucker Balch, Prashant Reddy, and Manuela Veloso · 2020
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A data-driven market simulator for small data environments
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Learning spatial-semantic context with fully convolutional recurrent network for online handwritten chinese text recognition
Zecheng Xie, Zenghui Sun, Lianwen Jin, Hao Ni, and Terry Lyons · 2017
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Leveraging the path signature for skeleton-based human action recognition
Weixin Yang, Terry Lyons, Hao Ni, Cordelia Schmid, Lianwen Jin, and Jiawei Chang · 2017
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The limit points of (optimistic) gradient descent in min-max optimization
Constantinos Daskalakis and Ioannis Panageas · 2018
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Sample complexity of sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2018
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Real-valued (medical) time series generation with recurrent conditional gans
Stephanie Hyland, Cristóbal Esteban, and Gunnar Rätsch · 2018
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Cycles in adversarial regularized learning
Panayotis Mertikopoulos, Christos Papadimitriou, and Georgios Piliouras · 2018
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Which training methods for gans do actually converge?
Lars Mescheder, Andreas Geiger, and Sebastian Nowozin · 2018
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Hans Buehler, Blanka Horvath, Terry Lyons, Imanol Perez Arribas, and Ben Wood · 2020
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A generative adversarial network approach to calibration of local stochastic volatility models
Christa Cuchiero, Wahid Khosrawi, and Josef Teichmann · 2020
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Gans may have no nash equilibria
Farzan Farnia and Asuman Ozdaglar · 2020
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Robust pricing and hedging via neural sdes
Patryk Gierjatowicz, Marc Sabate-Vidales, David Siska, Lukasz Szpruch, and Zan Zuric · 2020
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If you like it, gan it. probabilistic multivariate times series forecast with gan
Alireza Koochali, Andreas Dengel, and Sheraz Ahmed · 2020
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On gradient descent ascent for nonconvex-concave minimax problems
Tianyi Lin, Chi Jin, and Michael Jordan · 2020
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Generating high-fidelity synthetic patient data for assessing machine learning healthcare software
Allan Tucker, Zhenchen Wang, Ylenia Rotalinti, and Puja Myles · 2020
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Quant gans: deep generation of financial time series
Magnus Wiese, Robert Knobloch, Ralf Korn, and Peter Kretschmer · 2020
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The expected signature of brownian motion stopped on the boundary of a circle has finite radius of convergence
Horatio Boedihardjo, Joscha Diehl, Marc Mezzarobba, and Hao Ni · 2021
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Sig-wasserstein gans for time series generation
Hao Ni, Lukasz Szpruch, Marc Sabate-Vidales, Baoren Xiao, Magnus Wiese, and Shujian Liao · 2021
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Signature moments to characterize laws of stochastic processes
Ilya Chevyrev and Harald Oberhauser · 2022
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Functional linear regression with truncated signatures
Adeline Fermanian · 2022
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Expected signature of stopped Brownian motion on d-dimensional C 2 , α {C}^{2,\alpha} -domains has finite radius of convergence everywhere: 2 ≤ d ≤ 8 2\leq d\leq 8
Siran Li and Hao Ni · 2022
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