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2022-10-06 12:25:40 +00:00
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}
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}
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month = {12},
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2022-10-06 12:25:40 +00:00
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2024-03-19 12:30:44 +00:00
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2022-10-11 17:09:55 +00:00
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}
2024-03-19 12:30:44 +00:00
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author = {Donald S. Burdick}
}
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author = {Comon, Pierre},
isbn = {9780198507345},
title = {{Tensor Decompositions: State of the Art and Applications}},
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year = {2002},
month = {06},
doi = {10.1093/oso/9780198507345.003.0001},
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}
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author = {Comon, Pierre},
booktitle = {2009 IEEE/SP 15th Workshop on Statistical Signal Processing},
title = {Tensors versus matrices usefulness and unexpected properties},
year = {2009},
volume = {},
number = {},
pages = {781-788},
doi = {10.1109/SSP.2009.5278471}
}
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author = {Cook, R. Dennis},
journal = {Statistical Science},
month = {02},
number = {1},
pages = {1--26},
publisher = {The Institute of Mathematical Statistics},
title = {{Fisher Lecture: Dimension Reduction in Regression}},
volume = {22},
year = {2007},
doi = {10.1214/088342306000000682}
}
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title = {Multivariate bernoulli distribution models},
year = {2012}
}
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year = {2013}
}
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ISSN = {00063444},
URL = {http://www.jstor.org/stable/2335827},
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author = {A. P. Dawid},
journal = {Biometrika},
number = {1},
pages = {265--274},
publisher = {[Oxford University Press, Biometrika Trust]},
title = {Some Matrix-Variate Distribution Theory: Notational Considerations and a Bayesian Application},
urldate = {2024-01-12},
volume = {68},
year = {1981}
}
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number = {2},
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year = {2007},
note = {Tensor Signal Processing},
issn = {0165-1684},
doi = {https://doi.org/10.1016/j.sigpro.2005.12.014},
url = {https://www.sciencedirect.com/science/article/pii/S0165168406001757},
author = {André L.F. {de Almeida} and Gérard Favier and João Cesar M. Mota}
}
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title = {A Statistically Identifiable Model for Tensor-Valued Gaussian Random Variables},
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year = {2019},
volume = {abs/1911.02915},
url = {https://api.semanticscholar.org/CorpusID:207847615}
}
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volume = {87},
number = {2},
pages = {322-336},
year = {2007},
note = {Tensor Signal Processing},
issn = {0165-1684},
doi = {10.1016/j.sigpro.2005.12.015},
url = {https://www.sciencedirect.com/science/article/pii/S0165168406001745},
author = {Lieven {De Lathauwer} and Joséphine Castaing}
}
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2022-10-11 17:09:55 +00:00
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year = {2015},
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doi = {10.1016/j.jmva.2014.08.015}
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2024-03-19 12:30:44 +00:00
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}
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}
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}
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year = {2012}
}
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doi = {10.1214/11-BA606}
}
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2022-10-06 12:25:40 +00:00
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2024-03-19 12:30:44 +00:00
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}
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@book { Kusolitsch2011 ,
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2023-11-14 13:35:43 +00:00
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2023-11-14 13:35:43 +00:00
title = {Introduction to Riemannian Manifolds},
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}
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journal = {IEEE Transactions on Medical Imaging},
title = {Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors},
year = {2008},
volume = {27},
number = {1},
pages = {129-141},
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2023-11-14 13:35:43 +00:00
}
2024-03-19 12:30:44 +00:00
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title = {{Multilinear Models: Applications in Spectroscopy}},
author = {Sue Leurgans and Robert T. Ross},
year = {1992},
journal = {Statistical Science},
volume = {7},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {289 -- 310},
keywords = {Multi-mode factor analysis, nonlinear least-squares, PARAFAC, three-way arrays},
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2023-11-14 13:35:43 +00:00
}
2024-03-19 12:30:44 +00:00
@article { LengPan2018 ,
author = {Leng, Chenlei and Pan, Guangming},
title = {{Covariance estimation via sparse Kronecker structures}},
volume = {24},
journal = {Bernoulli},
number = {4B},
publisher = {Bernoulli Society for Mathematical Statistics and Probability},
pages = {3833 -- 3863},
year = {2018},
doi = {10.3150/17-BEJ980}
}
@article { LeporeEtAt2008 ,
author = {Lepore, Natasha and Brun, Caroline and Chou, Yi-Yu and Chiang, Ming-Chang and Dutton, Rebecca A. and Hayashi, Kiralee M. and Luders, Eileen and Lopez, Oscar L. and Aizenstein, Howard J. and Toga, Arthur W. and Becker, James T. and Thompson, Paul M.},
journal = {IEEE Transactions on Medical Imaging},
title = {Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors},
year = {2008},
volume = {27},
number = {1},
pages = {129-141},
doi = {10.1109/TMI.2007.906091}
}
@article { LeurgansRoss1992 ,
title = {{Multilinear Models: Applications in Spectroscopy}},
author = {Sue Leurgans and Robert T. Ross},
year = {1992},
journal = {Statistical Science},
volume = {7},
number = {3},
publisher = {Institute of Mathematical Statistics},
pages = {289 -- 310},
keywords = {Multi-mode factor analysis, nonlinear least-squares, PARAFAC, three-way arrays},
doi = {10.1214/ss/1177011225}
}
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title = {Sliced Inverse Regression for Dimension Reduction},
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volume = {86},
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year = {1991},
}
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author = {Ker-Chau Li},
title = {On Principal Hessian Directions for Data Visualization and Dimension Reduction: Another Application of Stein's Lemma},
journal = {Journal of the American Statistical Association},
volume = {87},
number = {420},
pages = {1025-1039},
year = {1992},
publisher = {Taylor \& Francis},
doi = {10.1080/01621459.1992.10476258},
}
@article { LiKimAltman2010 ,
author = {Bing Li and Min Kyung Kim and Naomi Altman},
title = {{On dimension folding of matrix- or array-valued statistical objects}},
volume = {38},
journal = {The Annals of Statistics},
number = {2},
publisher = {Institute of Mathematical Statistics},
pages = {1094 -- 1121},
keywords = {directional regression, electroencephalography, Kronecker envelope, sliced average variance estimate, sliced inverse regression},
year = {2010},
doi = {10.1214/09-AOS737}
}
# TODO: check this!
@inbook { LiuKoike2007 ,
title = {Extending Multivariate Space-Time Geostatistics for Environmental Data Analysis},
author = {Chunxue Liu and Katsuaki Koike},
year = {2007},
journal = {Mathematical Geology},
publisher = {International Association for Mathematical Geology},
pages = {289--305},
doi = {10.1007/s11004-007-9085-9}
}
@article { LuZimmerman2005 ,
title = {The likelihood ratio test for a separable covariance matrix},
author = {Nelson Lu and Dale L. Zimmerman},
year = {2005},
journal = {Statistics \& Probability Letters},
volume = {73},
number = {4},
pages = {449-457},
issn = {0167-7152},
doi = {10.1016/j.spl.2005.04.020},
url = {https://www.sciencedirect.com/science/article/pii/S0167715205001495}
}
@article { MagnusNeudecker1986 ,
title = {Symmetry, 0-1 Matrices and Jacobians: A Review},
author = {Magnus, Jan R. and Neudecker, Heinz},
ISSN = {02664666, 14694360},
URL = {http://www.jstor.org/stable/3532421},
journal = {Econometric Theory},
number = {2},
pages = {157--190},
publisher = {Cambridge University Press},
urldate = {2023-10-03},
volume = {2},
year = {1986}
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}
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@book { MagnusNeudecker1999 ,
title = {Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition)},
author = {Magnus, Jan R. and Neudecker, Heinz},
year = {1999},
publisher = {John Wiley \& Sons Ltd},
isbn = {0-471-98632-1}
}
@article { ManceurDutilleul2013 ,
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title = {Maximum likelihood estimation for the tensor normal distribution: Algorithm, minimum sample size, and empirical bias and dispersion},
author = {Ameur M. Manceur and Pierre Dutilleul},
journal = {Journal of Computational and Applied Mathematics},
volume = {239},
pages = {37-49},
year = {2013},
issn = {0377-0427},
doi = {10.1016/j.cam.2012.09.017},
url = {https://www.sciencedirect.com/science/article/pii/S0377042712003810}
}
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@article { MardiaGoodall1993 ,
title = {Spatial-Temporal Analysis of Multivariate Environmental Monitoring Data},
author = {Mardia, Kanti and Goodall, Colin},
year = {1993},
month = {01},
pages = {},
volume = {6},
publisher = {Elsevier Science Publisher B.V.}
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}
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@InProceedings { MartinFernandez2004 ,
author = {Mart{\'i}n-Fern{\'a}ndez, Marcos and Westin, Carl-Fredrik and Alberola-L{\'o}pez, Carlos},
editor = {Barillot, Christian and Haynor, David R. and Hellier, Pierre},
title = {3D Bayesian Regularization of Diffusion Tensor MRI Using Multivariate Gaussian Markov Random Fields},
booktitle = {Medical Image Computing and Computer-Assisted Intervention -- MICCAI 2004},
year = {2004},
publisher = {Springer Berlin Heidelberg},
address = {Berlin, Heidelberg},
pages = {351--359},
abstract = {3D Bayesian regularization applied to diffusion tensor MRI is presented here. The approach uses Markov Random Field ideas and is based upon the definition of a 3D neighborhood system in which the spatial interactions of the tensors are modeled. As for the prior, we model the behavior of the tensor fields by means of a 6D multivariate Gaussian local characteristic. As for the likelihood, we model the noise process by means of conditionally independent 6D multivariate Gaussian variables. Those models include inter-tensor correlations, intra-tensor correlations and colored noise. The solution tensor field is obtained by using the simulated annealing algorithm to achieve the maximum a posteriori estimation. Several experiments both on synthetic and real data are presented, and performance is assessed with mean square error measure.},
isbn = {978-3-540-30135-6}
}
@book { McCullagh1987 ,
title = {Tensor Methods in Statistics},
subtitle = {Monographs on Statistics and Applied Probability},
author = {McCullagh, Peter},
year = {1987},
publisher = {Chapman and Hall/CRC},
doi = {10.1201/9781351077118}
}
@inproceedings { Nesterov1983 ,
title = {A method of solving a convex programming problem with convergence rate $O(1/k^2)$},
author = {Nesterov, Yurii Evgen'evich},
booktitle = {Doklady Akademii Nauk},
volume = {269},
number = {3},
pages = {543--547},
year = {1983},
organization= {Russian Academy of Sciences}
}
@article { OhlsonEtAt2013 ,
title = {The multilinear normal distribution: Introduction and some basic properties},
author = {Ohlson, Martin and Ahmad, Mumtaz Rauf and von Rosen, Dietrich},
year = {2013},
journal = {Journal of Multivariate Analysis},
volume = {113},
pages = {37-47},
issn = {0047-259X},
doi = {10.1016/j.jmva.2011.05.015},
url = {https://www.sciencedirect.com/science/article/pii/S0047259X11001047}
}
@article { PfeifferForzaniBura ,
author = {Pfeiffer, Ruth and Forzani, Liliana and Bura, Efstathia},
year = {2012},
month = {09},
pages = {2414-27},
title = {Sufficient dimension reduction for longitudinally measured predictors},
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volume = {31},
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journal = {Statistics in medicine},
doi = {10.1002/sim.4437}
}
@article { PfeifferKaplaBura2021 ,
author = {Pfeiffer, Ruth and Kapla, Daniel and Bura, Efstathia},
title = {{Least squares and maximum likelihood estimation of sufficient reductions in regressions with matrix-valued predictors}},
volume = {11},
year = {2021},
journal = {International Journal of Data Science and Analytics},
doi = {10.1007/s41060-020-00228-y}
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}
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@inproceedings { ShashuaHazan2005 ,
author = {Shashua, Amnon and Hazan, Tamir},
title = {Non-Negative Tensor Factorization with Applications to Statistics and Computer Vision},
year = {2005},
isbn = {1595931805},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
doi = {10.1145/1102351.1102451},
booktitle = {Proceedings of the 22nd International Conference on Machine Learning},
pages = {792--799},
numpages = {8},
location = {Bonn, Germany},
series = {ICML '05}
}
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@article { Soize2008 ,
title = {Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size},
author = {C. Soize},
year = {2008},
journal = {Probabilistic Engineering Mechanics},
volume = {23},
number = {2},
pages = {307-323},
note = {5th International Conference on Computational Stochastic Mechanics},
issn = {0266-8920},
doi = {10.1016/j.probengmech.2007.12.019},
url = {https://www.sciencedirect.com/science/article/pii/S0266892007000562}
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}
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@article { SoloveychikTrushin2016 ,
title = {Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness},
author = {I. Soloveychik and D. Trushin},
year = {2016},
journal = {Journal of Multivariate Analysis},
volume = {149},
pages = {92-113},
issn = {0047-259X},
doi = {10.1016/j.jmva.2016.04.001},
url = {https://www.sciencedirect.com/science/article/pii/S0047259X16300070}
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}
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@misc { SongHero2023 ,
title = {On Separability of Covariance in Multiway Data Analysis},
author = {Dogyoon Song and Alfred O. Hero},
year = {2023},
eprint = {2302.02415},
archivePrefix = {arXiv},
primaryClass = {math.ST},
doi = {10.48550/arXiv.2302.02415}
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}
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@article { SrivastavaEtAt2008 ,
title = {Models with a Kronecker product covariance structure: Estimation and testing},
author = {Srivastava, Muni Shanker and von Rosen, Tatjana and von Rosen, Dietrich},
year = {2008},
journal = {Mathematical Methods of Statistics},
month = {Dec},
day = {01},
volume = {17},
number = {4},
pages = {357-370},
issn = {1934-8045},
doi = {10.3103/S1066530708040066}
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}
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@book { SrivastavaKhatri1979 ,
title = {An introduction to multivariate statistics},
author = {Srivastava, Muni Shanker and Khatri, Chinubal G.},
year = {1979},
publisher = {North Holland},
isbn = {0444003029},
language = {eng},
address = {New York, NY [u.a.]}
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}
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@article { TsiligkaridisHero2013 ,
author = {Tsiligkaridis, Theodoros and Hero, Alfred O.},
journal = {IEEE Transactions on Signal Processing},
title = {Covariance Estimation in High Dimensions Via Kronecker Product Expansions},
year = {2013},
volume = {61},
number = {21},
pages = {5347-5360},
doi = {10.1109/TSP.2013.2279355}
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}
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@Inbook { Uschmajew2020 ,
author = {Uschmajew, Andr{\'e} and Vandereycken, Bart},
editor = {Grohs, Philipp and Holler, Martin and Weinmann, Andreas},
title = {Geometric Methods on Low-Rank Matrix and Tensor Manifolds},
bookTitle = {Handbook of Variational Methods for Nonlinear Geometric Data},
year = {2020},
publisher = {Springer International Publishing},
address = {Cham},
pages = {261--313},
isbn = {978-3-030-31351-7},
doi = {10.1007/978-3-030-31351-7_9}
}
@book { vanderVaart1998 ,
title = {Asymptotic Statistics},
author = {{van der Vaart}, A.W.},
series = {Asymptotic Statistics},
year = {1998},
publisher = {Cambridge University Press},
series = {Cambridge Series in Statistical and Probabilistic Mathematics},
isbn = {0-521-49603-9}
}
@Inbook { VanLoanPitsianis1993 ,
author = {Van Loan, C. F. and Pitsianis, N.},
editor = {Moonen, Marc S. and Golub, Gene H. and De Moor, Bart L. R.},
title = {Approximation with Kronecker Products},
bookTitle = {Linear Algebra for Large Scale and Real-Time Applications},
year = {1993},
publisher = {Springer Netherlands},
address = {Dordrecht},
pages = {293--314},
isbn = {978-94-015-8196-7},
doi = {10.1007/978-94-015-8196-7_17}
}
@article { WangEtAt2022 ,
author = {Yu Wang and Zeyu Sun and Dogyoon Song and Alfred Hero},
title = {{Kronecker-structured covariance models for multiway data}},
volume = {16},
journal = {Statistics Surveys},
number = {none},
publisher = {Amer. Statist. Assoc., the Bernoulli Soc., the Inst. Math. Statist., and the Statist. Soc. Canada},
pages = {238 -- 270},
year = {2022},
doi = {10.1214/22-SS139}
}
# arXiv version: https://doi.org/10.48550/arXiv.1811.05076
@article { WangLi2020 ,
title = {Learning from Binary Multiway Data: Probabilistic Tensor Decomposition and its Statistical Optimality},
author = {Miaoyan Wang and Lexin Li},
year = {2020},
journal = {Journal of Machine Learning Research},
volume = {21},
number = {154},
pages = {1--38}
}
% TODO: check
@book { Whittaker2009 ,
author = {J. Whittaker},
title = {Graphical Models in Applied Multivariate Statistics},
publisher = {Wiley},
year = {2009}
}
@article { ZhangZhou2005 ,
title = {(2D)2PCA: Two-directional two-dimensional PCA for efficient face representation and recognition},
journal = {Neurocomputing},
volume = {69},
number = {1},
pages = {224-231},
year = {2005},
note = {Neural Networks in Signal Processing},
issn = {0925-2312},
doi = {https://doi.org/10.1016/j.neucom.2005.06.004},
url = {https://www.sciencedirect.com/science/article/pii/S0925231205001785},
author = {Daoqiang Zhang and Zhi-Hua Zhou}
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}
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@article { ZhouLi2014 ,
author = {Zhou, Hua and Li, Lexin},
title = {Regularized matrix regression},
journal = {Journal of the Royal Statistical Society. Series B (Statistical Methodology)},
volume = {76},
number = {2},
pages = {463--483},
year = {2014},
publisher = {[Royal Statistical Society, Wiley]}
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}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Software, data Sets, ... %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@misc { lichess-database ,
author = {Thibault Duplessis},
title = {lichess.org open database},
year = {2013},
url = {https://database.lichess.org},
note = {visited on December 8, 2023},
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}
@Article { Rdimtools ,
title = {{Rdimtools}: An {R} Package for Dimension Reduction and Intrinsic Dimension Estimation},
author = {Kisung You and Dennis Shung},
journal = {Software Impacts},
year = {2022},
volume = {14},
issn = {26659638},
pages = {100414},
doi = {10.1016/j.simpa.2022.100414},
}
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@mish { schachhoernchen ,
title = {Schach H\"ornchen},
year = {development since 2021, first release pending},
author = {Daniel Kapla},
url = {todo!}
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}
@misc { stockfish ,
title = {Stockfish},
year = {since 2008},
author = {{The Stockfish developers (see \href{https://github.com/official-stockfish/Stockfish/blob/master/AUTHORS}{AUTHORS} file)}},
url = {https://stockfishchess.org/},
abstract = {Stockfish is a free and strong UCI chess engine.},
}
