Introduction to vector quantization and its applications for numerics
ESAIM: Proc., 48 (2015) 29-79
Published online: 2015-03-09
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Mean Squared Error Representative Points of Pareto Distributions and Their Estimation
Xinyang Li and Xiaoling PengEntropy 27 (3) 249 (2025)
https://doi.org/10.3390/e27030249
A new class of moment-constrained mean square error representative samples for continuous distributions
Xinyang Li, Ping He, Moyuan Huang and Xiaoling PengJournal of Statistical Computation and Simulation 1 (2025)
https://doi.org/10.1080/00949655.2025.2485290
Asymptotic quantization of measures on Riemannian manifolds via covering growth estimates
Ata Deniz Aydın and Mikaela IacobelliAdvances in Mathematics 474 110311 (2025)
https://doi.org/10.1016/j.aim.2025.110311
On the Sequential Convergence of Lloyd’s Algorithms
Leo Portales, Elsa Cazelles and Edouard PauwelsMathematics of Operations Research (2025)
https://doi.org/10.1287/moor.2024.0550
A new Kolmogorov-Smirnov test based on representative points in the exponential distribution family
Yangyi Zhang, Sirao Wang, Xiao Ke and Huajun YeJournal of Statistical Computation and Simulation 94 (15) 3391 (2024)
https://doi.org/10.1080/00949655.2024.2385687
The resampling method via representative points
Long-Hao Xu, Yinan Li and Kai-Tai FangStatistical Papers 65 (6) 3621 (2024)
https://doi.org/10.1007/s00362-024-01536-2
(2024)
https://doi.org/10.32388/DX6MDB
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing
Sebastian Becker, Arnulf Jentzen, Marvin S. Müller and Philippe von WurstembergerMathematical Finance 34 (1) 90 (2024)
https://doi.org/10.1111/mafi.12405
Minimum energy representative points
A.M. Elsawah, Yi-An Wang and Fatih TankJournal of Computational and Applied Mathematics 438 115526 (2024)
https://doi.org/10.1016/j.cam.2023.115526
Quantization of stochastic volatility models: Numerical tests and an open source implementation
Alessandro Fina, Alessandro Gnoatto and Athena PicarelliMathematics and Computers in Simulation 225 29 (2024)
https://doi.org/10.1016/j.matcom.2024.04.030
A fully quantization-based scheme for FBSDEs
Giorgia Callegaro, Alessandro Gnoatto and Martino GrasselliApplied Mathematics and Computation 441 127666 (2023)
https://doi.org/10.1016/j.amc.2022.127666
Limiting behavior of the gap between the largest two representative points of statistical distributions
Long-Hao Xu, Kai-Tai Fang and Jianxin PanCommunications in Statistics - Theory and Methods 52 (10) 3290 (2023)
https://doi.org/10.1080/03610926.2021.1970772
New Approaches on Parameter Estimation of the Gamma Distribution
Xiao Ke, Sirao Wang, Min Zhou and Huajun YeMathematics 11 (4) 927 (2023)
https://doi.org/10.3390/math11040927
Quantization dimensions of compactly supported probability measures via Rényi dimensions
Marc Kesseböhmer, Aljoscha Niemann and Sanguo ZhuTransactions of the American Mathematical Society 376 (7) 4661 (2023)
https://doi.org/10.1090/tran/8863
A Sampling Criterion for Constrained Bayesian Optimization with Uncertainties
Reda El Amri, Rodolphe Le Riche, Céline Helbert, Christophette Blanchet-Scalliet and Sébastien Da VeigaThe SMAI Journal of computational mathematics 9 285 (2023)
https://doi.org/10.5802/smai-jcm.102
2270 (2023)
https://doi.org/10.1109/CDC49753.2023.10384010
Quantum Information Dimension and Geometric Entropy
Fabio Anza and James P. CrutchfieldPRX Quantum 3 (2) (2022)
https://doi.org/10.1103/PRXQuantum.3.020355
Machine Learning, Optimization, and Data Science
Shun Matsuura and Hiroshi KurataLecture Notes in Computer Science, Machine Learning, Optimization, and Data Science 13163 430 (2022)
https://doi.org/10.1007/978-3-030-95467-3_31
Reweighting samples under covariate shift using a Wasserstein distance criterion
Julien Reygner and Adrien TouboulElectronic Journal of Statistics 16 (1) (2022)
https://doi.org/10.1214/21-EJS1974
Properties and generation of representative points of the exponential distribution
Long-Hao Xu, Kai-Tai Fang and Ping HeStatistical Papers 63 (1) 197 (2022)
https://doi.org/10.1007/s00362-021-01236-1
Brain Inspired Cortical Coding Method for Fast Clustering and Codebook Generation
Meric Yucel, Serdar Bagis, Ahmet Sertbas, Mehmet Sarikaya and Burak UstundagEntropy 24 (11) 1678 (2022)
https://doi.org/10.3390/e24111678
New approach to greedy vector quantization
Rancy El Nmeir, Harald Luschgy and Gilles PagèsBernoulli 28 (1) (2022)
https://doi.org/10.3150/21-BEJ1350
Convex Order, Quantization and Monotone Approximations of ARCH Models
Benjamin Jourdain and Gilles PagèsJournal of Theoretical Probability 35 (4) 2480 (2022)
https://doi.org/10.1007/s10959-021-01141-1
Millimeter Wave Beamforming Codebook Design via Learning Channel Covariance Matrices Over Riemannian Manifolds
Imtiaz Nasim and Ahmed S. IbrahimIEEE Access 10 119617 (2022)
https://doi.org/10.1109/ACCESS.2022.3222032
Adaptive force biasing algorithms: New convergence results and tensor approximations of the bias
Virginie Ehrlacher, Tony Lelièvre and Pierre MonmarchéThe Annals of Applied Probability 32 (5) (2022)
https://doi.org/10.1214/21-AAP1775
Three kinds of discrete approximations of statistical multivariate distributions and their applications
Jun Yang, Ping He and Kai-Tai FangJournal of Multivariate Analysis 188 104829 (2022)
https://doi.org/10.1016/j.jmva.2021.104829
Quantization goes polynomial
Giorgia Callegaro, Lucio Fiorin and Andrea PallaviciniQuantitative Finance 21 (3) 361 (2021)
https://doi.org/10.1080/14697688.2020.1828608
Weak and strong error analysis of recursive quantization: a general approach with an application to jump diffusions
Gilles Pagès and Abass SagnaIMA Journal of Numerical Analysis 41 (4) 2668 (2021)
https://doi.org/10.1093/imanum/draa033
Multiple yield curve modelling with CBI processes
Claudio Fontana, Alessandro Gnoatto and Guillaume SzuldaMathematics and Financial Economics 15 (3) 579 (2021)
https://doi.org/10.1007/s11579-020-00289-4
Determinantal Point Processes for Image Processing
Claire Launay, Agnès Desolneux and Bruno GalerneSIAM Journal on Imaging Sciences 14 (1) 304 (2021)
https://doi.org/10.1137/20M1327306
Optimal dual quantizers of 1D log-concave distributions: Uniqueness and Lloyd like algorithm
Benjamin Jourdain and Gilles PagèsJournal of Approximation Theory 267 105581 (2021)
https://doi.org/10.1016/j.jat.2021.105581
Handbook of Research on Multimedia Cyber Security
Reinaldo Padilha França, Yuzo Iano, Ana Carolina Borges Monteiro and Rangel ArthurAdvances in Information Security, Privacy, and Ethics, Handbook of Research on Multimedia Cyber Security 1 (2020)
https://doi.org/10.4018/978-1-7998-2701-6.ch001
New weak error bounds and expansions for optimal quantization
Vincent Lemaire, Thibaut Montes and Gilles PagèsJournal of Computational and Applied Mathematics 371 112670 (2020)
https://doi.org/10.1016/j.cam.2019.112670
Conic quantization: stochastic volatility and market implied liquidity
Lucio Fiorin and Wim SchoutensQuantitative Finance 20 (4) 531 (2020)
https://doi.org/10.1080/14697688.2019.1687928
Approximation of Densities on Riemannian Manifolds
Alice le Brigant and Stéphane PuechmorelEntropy 21 (1) 43 (2019)
https://doi.org/10.3390/e21010043
Quantization and clustering on Riemannian manifolds with an application to air traffic analysis
Alice Le Brigant and Stéphane PuechmorelJournal of Multivariate Analysis 173 685 (2019)
https://doi.org/10.1016/j.jmva.2019.05.008
Conic Quantization: Stochastic Volatility and Market Implied Liquidity
Lucio Fiorin and Wim SchoutensSSRN Electronic Journal (2019)
https://doi.org/10.2139/ssrn.3325834
Quantization meets Fourier: a new technology for pricing options
Giorgia Callegaro, Lucio Fiorin and Martino GrasselliAnnals of Operations Research 282 (1-2) 59 (2019)
https://doi.org/10.1007/s10479-018-3048-z
Recursive marginal quantization of higher-order schemes
T. A. McWalter, R. Rudd, J. Kienitz and E. PlatenQuantitative Finance 18 (4) 693 (2018)
https://doi.org/10.1080/14697688.2017.1402125
Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering
Gilles Pagès and Abass SagnaStochastic Processes and their Applications 128 (3) 847 (2018)
https://doi.org/10.1016/j.spa.2017.05.009
A backward Monte Carlo approach to exotic option pricing
G. BORMETTI, G. CALLEGARO, G. LIVIERI and A. PALLAVICINIEuropean Journal of Applied Mathematics 29 (1) 146 (2018)
https://doi.org/10.1017/S0956792517000079
Uniform decomposition of probability measures: quantization, clustering and rate of convergence
Julien ChevallierJournal of Applied Probability 55 (4) 1037 (2018)
https://doi.org/10.1017/jpr.2018.69
Recursive Marginal Quantization of Higher-Order Schemes
Thomas A McWalter and Joerg KienitzSSRN Electronic Journal (2017)
https://doi.org/10.2139/ssrn.2894753
Quantization Meets Fourier: A New Technology for Pricing Options
Giorgia Callegaro, Lucio Fiorin and Martino GrasselliSSRN Electronic Journal (2017)
https://doi.org/10.2139/ssrn.2951755
Fast Quantization of Stochastic Volatility Models
Ralph Rudd, Thomas A McWalter, Joerg Kienitz and Eckhard PlatenSSRN Electronic Journal (2017)
https://doi.org/10.2139/ssrn.2956168
Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension
Gilles Pagès and Jun YuSIAM Journal on Control and Optimization 54 (5) 2354 (2016)
https://doi.org/10.1137/151005622
Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process
Gilles Pagès and Abass SagnaApplied Mathematical Finance 22 (5) 463 (2015)
https://doi.org/10.1080/1350486X.2015.1091741
A Backward Monte Carlo Approach to Exotic Option Pricing
Giacomo Bormetti, Giorgia Callegaro, Giulia Livieri and Andrea PallaviciniSSRN Electronic Journal (2015)
https://doi.org/10.2139/ssrn.2686115
https://doi.org/10.1002/9781119145066.biblio
Pricing and Calibration in Local Volatility Models Via Fast Quantization
Giorgia Callegaro, Lucio Fiorin and Martino GrasselliSSRN Electronic Journal (2014)
https://doi.org/10.2139/ssrn.2495829