@article{KoldaBader2009,
author = {Kolda, Tamara G. and Bader, Brett W.},
title = {Tensor Decompositions and Applications},
journal = {SIAM Review},
volume = {51},
number = {3},
pages = {455-500},
year = {2009},
doi = {10.1137/07070111X},
URL = { 
https://doi.org/10.1137/07070111X},
eprint ={https://doi.org/10.1137/07070111X},
abstract = { This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with \$N \geq 3\$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors. }
}

@article{RegMatrixReg-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]}
}

@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}
}

@book{StatInf-CasellaBerger2002,
    title       = {{Statistical Inference}},
    author      = {Casella, George and Berger, Roger L.},
    isbn        = {0-534-24312-6},
    series      = {Duxbury Advanced Series},
    year        = {2002},
    edition     = {2},
    publisher   = {Thomson Learning}
}

@book{MatrixDiffCalc-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{SymMatandJacobians-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}
}

@book{MatrixAlgebra-AbadirMagnus2005,
    title       = {Matrix Algebra},
    author      = {Abadir, Karim M. and Magnus, Jan R.},
    year        = {2005},
    publisher   = {Cambridge University Press},
    series      = {Econometric Exercises},
    collection  = {Econometric Exercises},
    place       = {Cambridge},
    doi         = {10.1017/CBO9780511810800}
}

@article{TensorDecomp-HuLeeWang2022,
    author      = {Hu, Jiaxin and Lee, Chanwoo and Wang, Miaoyan},
    title       = {Generalized Tensor Decomposition With Features on Multiple Modes},
    journal     = {Journal of Computational and Graphical Statistics},
    volume      = {31},
    number      = {1},
    pages       = {204-218},
    year        = {2022},
    publisher   = {Taylor \& Francis},
    doi         = {10.1080/10618600.2021.1978471},
}

@article{CovarEstSparseKron-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{sdr-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}
}

@article{sdr-BuraDuarteForzani2016,
    author      = {Bura, Efstathia and Duarte, Sabrina and Forzani, Liliana},
    title       = {Sufficient Reductions in Regressions With Exponential Family Inverse Predictors},
    journal     = {Journal of the American Statistical Association},
    volume      = {111},
    number      = {515},
    pages       = {1313-1329},
    year        = {2016},
    publisher   = {Taylor \& Francis},
    doi         = {10.1080/01621459.2015.1093944}
}

@article{FisherLectures-Cook2007,
    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}
}

@article{asymptoticMLE-BuraEtAl2018,
    author      = {Bura, Efstathia and Duarte, Sabrina and Forzani, Liliana and E. Smucler and M. Sued},
    title       = {Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models},
    journal     = {Statistics},
    volume      = {52},
    number      = {5},
    pages       = {1005-1024},
    year        = {2018},
    publisher   = {Taylor \& Francis},
    doi         = {10.1080/02331888.2018.1467420},
}

@article{tsir-DingCook2015,
    author      = {Shanshan Ding and R. Dennis Cook},
    title       = {Tensor sliced inverse regression},
    journal     = {Journal of Multivariate Analysis},
    volume      = {133},
    pages       = {216-231},
    year        = {2015},
    issn        = {0047-259X},
    doi         = {10.1016/j.jmva.2014.08.015}
}

@article{lsir-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},
    volume      = {31},
    journal     = {Statistics in medicine},
    doi         = {10.1002/sim.4437}
}

@Inbook{ApproxKron-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}
}

@book{asymStats-van_der_Vaart1998,
    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}
}

@book{measureTheory-Kusolitsch2011,
    title       = {{M}a\ss{}- und {W}ahrscheinlichkeitstheorie},
    subtitle    = {{E}ine {E}inf{\"u}hrung},
    author      = {Kusolitsch, Norbert},
    series      = {Springer-Lehrbuch},
    year        = {2011},
    publisher   = {Springer Vienna},
    isbn        = {978-3-7091-0684-6},
    doi         = {10.1007/978-3-7091-0685-3}
}

@book{optimMatrixMani-AbsilEtAl2007,
    title       = {{Optimization Algorithms on Matrix Manifolds}},
    author      = {Absil, P.-A. and Mahony, R. and Sepulchre, R.},
    year        = {2007},
    publisher   = {Princeton University Press},
    isbn        = {9780691132983},
    note        = {Full Online Text \url{https://press.princeton.edu/absil}}
}

@Inbook{geomMethodsOnLowRankMat-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{introToSmoothMani-Lee2012,
    title       = {Introduction to Smooth Manifolds},
    author      = {Lee, John M.},
    year        = {2012},
    journal     = {Graduate Texts in Mathematics},
    publisher   = {Springer New York},
    doi         = {10.1007/978-1-4419-9982-5}
}

@book{introToRiemannianMani-Lee2018,
    title       = {Introduction to Riemannian Manifolds},
    author      = {Lee, John M.},
    year        = {2018},
    journal     = {Graduate Texts in Mathematics},
    publisher   = {Springer International Publishing},
    doi         = {10.1007/978-3-319-91755-9}
}

@misc{MLEonManifolds-HajriEtAl2017,
    title       = {Maximum Likelihood Estimators on Manifolds},
    author      = {Hajri, Hatem and Said, Salem and Berthoumieu, Yannick},
    year        = {2017},
    journal     = {Lecture Notes in Computer Science},
    publisher   = {Springer International Publishing},
    pages       = {692-700},
    doi         = {10.1007/978-3-319-68445-1_80}
}

@article{relativity-Einstain1916,
    author      = {Einstein, Albert},
    title       = {Die Grundlage der allgemeinen Relativitätstheorie},
    year        = {1916},
    journal     = {Annalen der Physik},
    volume      = {354},
    number      = {7},
    pages       = {769-822},
    doi         = {10.1002/andp.19163540702}
}

@article{MultilinearOperators-Kolda2006,
    title       = {Multilinear operators for higher-order decompositions.},
    author      = {Kolda, Tamara Gibson},
    doi         = {10.2172/923081},
    url         = {https://www.osti.gov/biblio/923081},
    place       = {United States},
    year        = {2006},
    month       = {4},
    type        = {Technical Report}
}

@book{aufbauAnalysis-kaltenbaeck2021,
    title       = {Aufbau Analysis},
    author      = {Kaltenb\"ack, Michael},
    isbn        = {978-3-88538-127-3},
    series      = {Berliner Studienreihe zur Mathematik},
    edition     = {27},
    year        = {2021},
    publisher   = {Heldermann Verlag}
}

@article{TensorNormalMLE-ManceurDutilleul2013,
    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}
}

@article{StatIdentTensorGaussian-DeesMandic2019,
    title       = {A Statistically Identifiable Model for Tensor-Valued Gaussian Random Variables},
    author      = {Bruno Scalzo Dees and Danilo P. Mandic},
    journal     = {ArXiv},
    year        = {2019},
    volume      = {abs/1911.02915},
    url         = {https://api.semanticscholar.org/CorpusID:207847615}
}

@article{Ising-Ising1924,
    author      = {Ising, Ernst},
    title       = {{Beitrag zur Theorie des Ferromagnetismus}},
    journal     = {Zeitschrift f\"ur Physik},
    pages       = {253-258},
    volume      = {31},
    number      = {1},
    year        = {1924},
    month       = {2},
    issn        = {0044-3328},
    doi         = {10.1007/BF02980577}
}


# TODO: Fix the following!!!
@book{GraphicalModels-Whittaker2009,
    author      = {J. Whittaker},
    title       = {Graphical Models in Applied Multivariate Statistics},
    publisher   = {Wiley},
    year        = {2009}
}

@article{MVB-Dai2012,
    author      = {B. Dai},
    title       = {Multivariate bernoulli distribution models},
    year        = {2012}
}

@article{MVB-DaiDingWahba2013,
    author      = {B. Dai, S. Ding, and G. Wahba},
    title       = {Multivariate bernoulli distribution},
    year        = {2013}
}

@article{sdr-mixedPredictors-BuraForzaniEtAl2022,
    author      = {Bura and Forzani and TODO},
    title       = {Sufficient reductions in regression with mixed predictors},
    journal     = {},
    volume      = {},
    number      = {},
    year        = {2022}
}

@article{sparseIsing-ChengEtAt2014,
    author        = {J. Cheng, E. Levina, and J. Wang, P.and Zhu},
    title         = {A sparse Ising model with covariates},
    journal       = {},
    volume        = {},
    number        = {},
    year          = {2014},
    doi           = {10.1111/biom.12202}
}

@book{deeplearningbook-GoodfellowEtAl2016,
    title         = {Deep Learning},
    author        = {Ian Goodfellow and Yoshua Bengio and Aaron Courville},
    publisher     = {MIT Press},
    url           = {\url{http://www.deeplearningbook.org}},
    year          = {2016}
}

@misc{rmsprop-Hinton2012,
    title         = {Neural networks for machine learning},
    author        = {Hinton, G.},
    year          = {2012}
}

@article{self-kapla2019,
    title         = {Comparison of Different Word Embeddings and Neural Network Types for Sentiment Analysis of German Political Speeches},
    author        = {Kapla, Daniel},
    year          = {2019}
}

@article{MGCCA-GirkaEtAl2024,
    title         = {Tensor generalized canonical correlation analysis},
    author        = {Fabien Girka and Arnaud Gloaguen and Laurent {Le Brusquet} and Violetta Zujovic and Arthur Tenenhaus},
    year          = {2024},
    journal       = {Information Fusion},
    volume        = {102},
    issn          = {1566-2535},
    doi           = {10.1016/j.inffus.2023.102045}
}

@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},
}

@misc{lichess-database,
  author       = {{Thibault Duplessis}},
  title        = {lichess.org open database},
  year         = {2013},
  url          = {https://database.lichess.org},
  note         = {visited on December 8, 2023},
}

@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.},
}

@mish{schachhoernchen,
    title    = {Schach H\"ornchen},
    year     = {development since 2021, first release pending},
    author   = {Kapla, Daniel},
    url      = {todo!}
}