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The concentration of measure phenomena were discovered as the mathematical background of statistical mechanics at the end of the XIX - beginning of the XX century and were then explored in mathematics of the XX-XXI centuries.
Hilbert D. 1902 Mathematical problems. Bull. Amer. Math. Soc
1902
Earlier work this paper cites.
Hilbert D. 1902 The Foundations of Geometry
1902
Earlier work this paper cites.
Gibbs GW. 1960 [1902] Elementary Principles in Statistical Mechanics, Developed With Especial Reference to the Rational Foundation of Thermodynamics
1902
Earlier work this paper cites.
Corry L. 1997 David Hilbert and the axiomatization of physics (1894–1905). Arch. Hist. Exact Sci
1905
Earlier work this paper cites.
Von Neumann J. 1955 Mathematical Foundations of Quantum Mechanics
1932
Earlier work this paper cites.
Kolmogorov AN. 1956 Foundations of the Theory of Probability
1933
Earlier work this paper cites.
Fisher RA. 1936 The use of multiple measurements in taxonomic problems. Ann. Hum. Genet
1936
Earlier work this paper cites.
Oxtoby JC, Ulam SM. 1941 Measure-preserving homeomorphisms and metrical transitivity. Ann. Math
1941
Earlier work this paper cites.
Khinchin AY. 1949 Mathematical Foundations of Statistical Mechanics
1943
Earlier work this paper cites.
Giannopoulos AA, Milman VD. 2000 Concentration property on probability spaces. Adv. Math
1949
Earlier work this paper cites.
Lévy P. 1951 Problèmes concrets d’analyse fonctionnelle
1951
Earlier work this paper cites.
Rosenblatt F. 1962 Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms
1962
Earlier work this paper cites.
Hoeffding W. 1963. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc
1963
Earlier work this paper cites.
Jaynes ET. 1967 Foundations of probability theory and statistical mechanics. In Delaware Seminar in the Foundations of Physics
1967
Earlier work this paper cites.
Markus L, Meyer KR. 1974 Generic Hamiltonian Dynamical Systems are Neither Integrable Nor Ergodic
1974
Earlier work this paper cites.
Wightman AS. 1976 Hilbert’s sixth problem: Mathematical treatment of the axioms of physics. In Browder FE (ed.). Mathematical Developments Arising from Hilbert Problems. Proceedings of Symposia in Pure Mathematics. XXVIII
1976
Earlier work this paper cites.
Oja E. 1982 A simplified neuron model as a principal component analyzer. J. Math. Biol
1982
Earlier work this paper cites.
Johnson WB, Lindenstrauss J. 1984 Extensions of Lipschitz mappings into a Hilbert space. Contemp. Math
1984
Earlier work this paper cites.
Gorban AN. 1990 Training Neural Networks
1990
Earlier work this paper cites.
Kainen P, Kůrková V. 1993 Quasiorthogonal dimension of Euclidian spaces. Appl. Math. Lett
1993
Earlier work this paper cites.
Hecht-Nielsen R. 1994 Context vectors: General-purpose approximate meaning representations self-organized from raw data. In Zurada J, Marks R, Robinson C, eds. Computational Intelligence: Imitating Life
1994
Earlier work this paper cites.
Talagrand M. 1995 Concentration of measure and isoperimetric inequalities in product spaces. Publications Mathematiques de l’IHES
1995
Earlier work this paper cites.
Kainen PC.1997 Utilizing geometric anomalies of high dimension: when complexity makes computation easier. In Computer-Intensive Methods in Control and Signal Processing: The Curse of Dimensionality
1996
Earlier work this paper cites.
Dobrushin RL. 1997 A mathematical approach to foundations of statistical mechanics. Atti dei Convegni Lincei – Accademia Nazionale dei Lincei
1997
Earlier work this paper cites.
Ball K. 1997 An Elementary Introduction to Modern Convex Geometry
1997
Cited alongside, same era.
Batterman RW. 1998 Why equilibrium statistical mechanics works: universality and the renormalization group. Philos. Sci
1998
Cited alongside, same era.
Donoho DL. 2000 High-dimensional data analysis: The curses and blessings of dimensionality. AMS Math Challenges Lecture
2000
Cited alongside, same era.
Vapnik V. 2000 The Nature of Statistical Learning Theory
2000
Cited alongside, same era.
Hyvärinen A, Oja E. 2000 Independent component analysis: algorithms and applications. Neural Netw
2000
Cited alongside, same era.
Ledoux M. 2001 The Concentration of Measure Phenomenon
2001
Cited alongside, same era.
Pestov V. 2013 Is the k k -NN classifier in high dimensions affected by the curse of dimensionality? Comput. Math. Appl
2012
Later among the works it cites.
Mirkin B. 2012 Clustering: A Data Recovery Approach
2012
Later among the works it cites.
Duda RD, Hart PE, and Stork DG. 2012 Pattern classification
2012
Later among the works it cites.
Quian Quiroga, R. 2012 Concept cells: the building blocks of declarative memory functions. Nat. Rev. Neurosci
2012
Later among the works it cites.
Zinovyev A, Mirkes E. 2013. Data complexity measured by principal graphs. Comput. Math. Appl
2012
Later among the works it cites.
Jia Y. 2013 Caffe: An open source convolutional architecture for fast feature embedding
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Engel A, Van den Broeck C. 2001 Statistical Mechanics of Learning
2001
Cited alongside, same era.
De Freitas N, Andrieu C, Højen-Sørensen P, Niranjan M, Gee A. 2001 Sequential Monte Carlo methods for neural networks. In Sequential Monte Carlo Methods in Practice
2001
Cited alongside, same era.
Cucker F, Smale S. 2002 On the mathematical foundations of learning. Bull. Amer. Math. Soc
2002
Cited alongside, same era.
Kégl B. 2003 Intrinsic dimension estimation using packing numbers. In Advances in neural information processing systems
2002
Cited alongside, same era.
Gromov M. 2003 Isoperimetry of waists and concentration of maps. Geom. Funct. Anal
2003
Cited alongside, same era.
Dasgupta S, Gupta A. 2003 An elementary proof of a theorem of Johnson and Lindenstrauss. Random Structures & Algorithms
2003
Cited alongside, same era.
2013
Later among the works it cites.
Anderson J, Belkin M, Goyal N, Rademacher L, Voss J. 2014 The More, the Merrier: the Blessing of dimensionality for learning large Gaussian mixtures, Journal of Machine Learning Research: Workshop and Conference Proceedings
2014
Later among the works it cites.
Aggarwal CC. 2015 Data Mining: The Textbook
2015
Later among the works it cites.
Gorban AN, Tyukin I, Prokhorov D, Sofeikov K. 2016 Approximation with random bases: Pro et contra. Inf. Sci
2015
Later among the works it cites.
Chen T, Li M, Li Y, Lin M, Wang N, Xiao T, Xu B, Zhang C, Zhang Z. 2015 MXNet: A Flexible and Efficient Machine Learning Library for Heterogeneous Distributed Systems
2015
Later among the works it cites.
Abadi M, Agarwal A, Barham P et al. 2015 TensorFlow: Large-scale machine learning on heterogeneous systems
2015
Later among the works it cites.
Ison MJ, Quian Quiroga R, Fried I. 2015 Rapid encoding of new memories by individual neurons in the human brain. Neuron
2015
Later among the works it cites.
2016
Later among the works it cites.
Gorban AN, Mirkes EM, Zinovyev A. 2016. Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning. Neural Netw
2016
Later among the works it cites.
Gorban AN, Tyukin IY, Romanenko I. 2016. The blessing of dimensionality: Separation theorems in the thermodynamic limit. IFAC-PapersOnLine
2016
Later among the works it cites.
Team DD. 2016 Deeplearning4j: Open-source distributed deep learning for the JVM
2016
Later among the works it cites.
Moczko E, Mirkes EM, Ceceres C, Gorban AN, Piletsky S. 2016 Fluorescence-based assay as a new screening tool for toxic chemicals. Sci. Rep
2016
Later among the works it cites.
Wang D, Li M. 2017 Stochastic configuration networks: Fundamentals and algorithms. IEEE Trans. On Cybernetics
2017
Later among the works it cites.
Scardapane S, Wang D. 2017 Randomness in neural networks: an overview. WIREs Data Mining Knowl. Discov
2017
Later among the works it cites.
Kůrková V, Sanguineti M. 2017 Probabilistic lower bounds for approximation by shallow perceptron networks. Neural Netw
2017
Later among the works it cites.
Gorban AN, Tyukin IY. 2017 Stochastic separation theorems. Neural Netw
2017
Later among the works it cites.
2017
Later among the works it cites.