# zbMATH — the first resource for mathematics

## Vapnik, Vladimir Naumovich

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 Author ID: vapnik.vladimir-n Published as: Vapnik, V.; Vapnik, V. N.; Vapnik, Vladimir; Vapnik, Vladimir N.; Wapnik, W. N. External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
 Documents Indexed: 52 Publications since 1964, including 10 Books Biographic References: 1 Publication
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#### Co-Authors

 10 single-authored 23 Chervonenkis, Alekseĭ Yakovlevich 6 Izmailov, Rauf 2 Chapelle, Olivier 2 Cortes, Corinna 2 Stefanyuk, A. R. 1 Ajdu, F. A. 1 Barnhill, Stephen 1 Ben-Hur, Asa 1 Bengio, Yoshua 1 Bi, Jinbo 1 Blagoveshchenskiĭ, Yuriĭ Nikolaevich 1 Bousquet, Olivier 1 Braga, Igor 1 Dronfort, L. M. 1 Drucker, Harris 1 Glazkova, T. G. 1 Guyon, Isabelle 1 Horn, David 1 Jackel, L. D. 1 Koshcheev, V. A. 1 LeCun, Yann 1 Lerner, Alexander Ya. 1 Markovich, Natalia M. 1 Meshalkin, L. D. 1 Mikhal’skij, A. I. 1 Mukherjee, Sayan 1 Raudis, Sharunas 1 Siegelmann, Hava T. 1 Sterin, A. M. 1 Tel’ksnis, Laimutis A. 1 Vashist, Akshay 1 Weston, Jason
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#### Serials

 14 Automation and Remote Control 5 Machine Learning 4 Journal of Machine Learning Research (JMLR) 2 Theory of Probability and its Applications 1 Physica A 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Avtomatika i Telemekhanika 1 Soviet Mathematics. Doklady 1 Neural Networks 1 Neural Computation 1 Annals of Mathematics and Artificial Intelligence 1 Statistical Analysis and Data Mining 1 Springer Series in Statistics
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#### Fields

 29 Computer science (68-XX) 20 Statistics (62-XX) 9 Probability theory and stochastic processes (60-XX) 5 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH

41 Publications have been cited 4,585 times in 3,299 Documents Cited by Year
Statistical learning theory. Zbl 0935.62007
1998
The nature of statistical learning theory. Zbl 0833.62008
1995
Support-vector networks. Zbl 0831.68098
Cortes, Corinna; Vapnik, Vladimir
1995
The nature of statistical learning theory. 2nd ed. Zbl 0934.62009
Vapnik, V. N.
2000
On the uniform convergence of relative frequencies of events to their probabilities. Zbl 0247.60005
Vapnik, V. N.; Chervonenkis, A. Ya.
1971
Gene selection for cancer classification using support vector machines. Zbl 0998.68111
Guyon, Isabelle; Weston, Jason; Barnhill, Stephen; Vapnik, Vladimir
2002
Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz. Zbl 0499.62005
1982
Choosing multiple parameters for support vector machines. Zbl 0998.68101
Chapelle, Olivier; Vapnik, Vladimir; Bousquet, Olivier; Mukherjee, Sayan
2002
Theory of pattern recognition. Statistical problems of learning. Zbl 0284.68070
Vapnik, V. N.; Chervonenkis, A. Ya.
1974
The support vector method of function estimation. Zbl 0928.68093
Vapnik, V.
1999
Necessary and sufficient conditions for the uniform convergence of means to their expectations. Zbl 0487.60036
Vapnik, V. N.; Chervonenkis, A. Ya.
1982
Support vector clustering. Zbl 1002.68598
Ben-Hur, Asa; Horn, David; Siegelmann, Hava T.; Vapnik, Vladimir
2002
Reconstruction of functions from empirical data. Zbl 0499.62004
Vapnik, V. N.
1979
Estimation of dependences based on empirical data. Translated from the Russian by Samuel Kotz. With a new afterword of the 2006 ed.: Empirical inference science. 2nd ed., reprint of 1982 ed. Zbl 1118.62002
2006
A new learning paradigm: learning using privileged information. Zbl 1335.68212
Vapnik, Vladimir; Vashist, Akshay
2009
Necessary and sufficient conditions for the uniform convergence of empirical means to their true values. Zbl 0471.60041
Vapnik, V. N.; Chervonenkis, A. Ya.
1981
Model selection for small sample regression. Zbl 0998.68114
Chapelle, Olivier; Vapnik, Vladimir; Bengio, Yoshua
2002
Uniform convergence of frequencies of occurence of events to their probabilities. Zbl 0247.60004
Vapnik, V. N.; Chervonenkis, A. Ya.
1968
On the uniform convergence of relative frequencies of events to their probabilities. Zbl 1337.60009
Vapnik, V. N.; Chervonenkis, A. Ya.
2015
Boosting and other ensemble methods. Zbl 0939.68791
Drucker, Harris; Cortes, Corinna; Jackel, L. D.; LeCun, Yann; Vapnik, Vladimir
1994
Inductive principles of the search for empirical dependences. (Methods based on weak convergence of probability measures). Zbl 0746.68075
Vapnik, V. N.
1989
Theory of uniform convergence of frequencies of events to their probabilities and problems of search for an optimal solution from empirical data. Zbl 0249.62031
Vapnik, V. N.; Chervonenkis, A. Ya.
1971
Learning using privileged information: similarity control and knowledge transfer. Zbl 1351.68240
Vapnik, Vladimir; Izmailov, Rauf
2015
Algorithms and programs for the reconstruction of dependencies. Zbl 0599.62004
Vapnik, V. N.; Glazkova, T. G.; Koshcheev, V. A.; Mikhal’skiĭ, A. I.; Chervonenkis, A. Ya.
1984
Nonparametric methods for reconstructing probability densities. Zbl 0418.93071
Vapnik, V. N.; Stefanyuk, A. R.
1978
On a class of perceptrons. Zbl 0173.19103
Vapnik, V. N.; Chervonenkis, A. J.
1964
Theorie der Zeichenerkennung. Übers. a. d. Russ., in dtsch. Spr. hrsg. v. Siegfried Unger und Klaus Fritzsch. Zbl 0417.68071
Wapnik, W. N.; Tscherwonenkis, A. J.
1979
Ordered risk minimization. I. Zbl 0299.93050
Vapnik, V. N.; Chervonenkis, A. Ya.
1974
On the uniform convergence of the frequencies of occurrence of events to their probabilities. Zbl 1325.60006
Vapnik, Vladimir N.; Chervonenkis, Alexey Ya.
2013
Rate of convergence in $$L_ 2$$ of the projection estimator of the distribution density. Zbl 0790.62038
Vapnik, V. N.; Markovich, N. M.; Stefanyuk, A. R.
1992
On a class of pattern recognition learning algorithms. Zbl 0137.10601
Vapnik, V. N.; Chervonenkis, A. Ya.
1965
Complete statistical theory of learning. Zbl 1436.62712
Vapnik, V. N.
2019
Rethinking statistical learning theory: learning using statistical invariants. Zbl 07036671
Vapnik, Vladimir; Izmailov, Rauf
2019
Knowledge transfer in SVM and neural networks. Zbl 1422.68207
Vapnik, Vladimir; Izmailov, Rauf
2017
$$V$$-matrix method of solving statistical inference problems. Zbl 1351.62086
Vapnik, Vladimir; Izmailov, Rauf
2015
Learning with rigorous support vector machines. Zbl 1274.68291
Bi, Jinbo; Vapnik, Vladimir N.
2003
Three fundamental concepts of the capacity of learning machines. Zbl 0799.60032
Vapnik, V.
1993
Estimation of probability density on the basis of the method of stochastic regularization. Zbl 0692.62035
Ajdu, F. A.; Vapnik, V. N.
1989
Ordered minimization of total risk in a pattern-recognition problem. Zbl 0416.68082
Vapnik, V. N.; Sterin, A. M.
1977
Ordered risk minimization. II. Zbl 0304.93026
Vapnik, V. N.; Chervonenkis, A. Ya.
1974
Training von Maschinen zur Zeichenerkennung nach der Methode der verallgemeinerten Bildnisse. Zbl 0189.17001
Vapnik, V. N.; Lerner, A. J.; Chervonenkis, A. Ya.
1967
Complete statistical theory of learning. Zbl 1436.62712
Vapnik, V. N.
2019
Rethinking statistical learning theory: learning using statistical invariants. Zbl 07036671
Vapnik, Vladimir; Izmailov, Rauf
2019
Knowledge transfer in SVM and neural networks. Zbl 1422.68207
Vapnik, Vladimir; Izmailov, Rauf
2017
On the uniform convergence of relative frequencies of events to their probabilities. Zbl 1337.60009
Vapnik, V. N.; Chervonenkis, A. Ya.
2015
Learning using privileged information: similarity control and knowledge transfer. Zbl 1351.68240
Vapnik, Vladimir; Izmailov, Rauf
2015
$$V$$-matrix method of solving statistical inference problems. Zbl 1351.62086
Vapnik, Vladimir; Izmailov, Rauf
2015
On the uniform convergence of the frequencies of occurrence of events to their probabilities. Zbl 1325.60006
Vapnik, Vladimir N.; Chervonenkis, Alexey Ya.
2013
A new learning paradigm: learning using privileged information. Zbl 1335.68212
Vapnik, Vladimir; Vashist, Akshay
2009
Estimation of dependences based on empirical data. Translated from the Russian by Samuel Kotz. With a new afterword of the 2006 ed.: Empirical inference science. 2nd ed., reprint of 1982 ed. Zbl 1118.62002
2006
Learning with rigorous support vector machines. Zbl 1274.68291
Bi, Jinbo; Vapnik, Vladimir N.
2003
Gene selection for cancer classification using support vector machines. Zbl 0998.68111
Guyon, Isabelle; Weston, Jason; Barnhill, Stephen; Vapnik, Vladimir
2002
Choosing multiple parameters for support vector machines. Zbl 0998.68101
Chapelle, Olivier; Vapnik, Vladimir; Bousquet, Olivier; Mukherjee, Sayan
2002
Support vector clustering. Zbl 1002.68598
Ben-Hur, Asa; Horn, David; Siegelmann, Hava T.; Vapnik, Vladimir
2002
Model selection for small sample regression. Zbl 0998.68114
Chapelle, Olivier; Vapnik, Vladimir; Bengio, Yoshua
2002
The nature of statistical learning theory. 2nd ed. Zbl 0934.62009
Vapnik, V. N.
2000
The support vector method of function estimation. Zbl 0928.68093
Vapnik, V.
1999
Statistical learning theory. Zbl 0935.62007
1998
The nature of statistical learning theory. Zbl 0833.62008
1995
Support-vector networks. Zbl 0831.68098
Cortes, Corinna; Vapnik, Vladimir
1995
Boosting and other ensemble methods. Zbl 0939.68791
Drucker, Harris; Cortes, Corinna; Jackel, L. D.; LeCun, Yann; Vapnik, Vladimir
1994
Three fundamental concepts of the capacity of learning machines. Zbl 0799.60032
Vapnik, V.
1993
Rate of convergence in $$L_ 2$$ of the projection estimator of the distribution density. Zbl 0790.62038
Vapnik, V. N.; Markovich, N. M.; Stefanyuk, A. R.
1992
Inductive principles of the search for empirical dependences. (Methods based on weak convergence of probability measures). Zbl 0746.68075
Vapnik, V. N.
1989
Estimation of probability density on the basis of the method of stochastic regularization. Zbl 0692.62035
Ajdu, F. A.; Vapnik, V. N.
1989
Algorithms and programs for the reconstruction of dependencies. Zbl 0599.62004
Vapnik, V. N.; Glazkova, T. G.; Koshcheev, V. A.; Mikhal’skiĭ, A. I.; Chervonenkis, A. Ya.
1984
Estimation of dependences based on empirical data. Transl. from the Russian by Samuel Kotz. Zbl 0499.62005
1982
Necessary and sufficient conditions for the uniform convergence of means to their expectations. Zbl 0487.60036
Vapnik, V. N.; Chervonenkis, A. Ya.
1982
Necessary and sufficient conditions for the uniform convergence of empirical means to their true values. Zbl 0471.60041
Vapnik, V. N.; Chervonenkis, A. Ya.
1981
Reconstruction of functions from empirical data. Zbl 0499.62004
Vapnik, V. N.
1979
Theorie der Zeichenerkennung. Übers. a. d. Russ., in dtsch. Spr. hrsg. v. Siegfried Unger und Klaus Fritzsch. Zbl 0417.68071
Wapnik, W. N.; Tscherwonenkis, A. J.
1979
Nonparametric methods for reconstructing probability densities. Zbl 0418.93071
Vapnik, V. N.; Stefanyuk, A. R.
1978
Ordered minimization of total risk in a pattern-recognition problem. Zbl 0416.68082
Vapnik, V. N.; Sterin, A. M.
1977
Theory of pattern recognition. Statistical problems of learning. Zbl 0284.68070
Vapnik, V. N.; Chervonenkis, A. Ya.
1974
Ordered risk minimization. I. Zbl 0299.93050
Vapnik, V. N.; Chervonenkis, A. Ya.
1974
Ordered risk minimization. II. Zbl 0304.93026
Vapnik, V. N.; Chervonenkis, A. Ya.
1974
On the uniform convergence of relative frequencies of events to their probabilities. Zbl 0247.60005
Vapnik, V. N.; Chervonenkis, A. Ya.
1971
Theory of uniform convergence of frequencies of events to their probabilities and problems of search for an optimal solution from empirical data. Zbl 0249.62031
Vapnik, V. N.; Chervonenkis, A. Ya.
1971
Uniform convergence of frequencies of occurence of events to their probabilities. Zbl 0247.60004
Vapnik, V. N.; Chervonenkis, A. Ya.
1968
Training von Maschinen zur Zeichenerkennung nach der Methode der verallgemeinerten Bildnisse. Zbl 0189.17001
Vapnik, V. N.; Lerner, A. J.; Chervonenkis, A. Ya.
1967
On a class of pattern recognition learning algorithms. Zbl 0137.10601
Vapnik, V. N.; Chervonenkis, A. Ya.
1965
On a class of perceptrons. Zbl 0173.19103
Vapnik, V. N.; Chervonenkis, A. J.
1964
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#### Cited by 6,499 Authors

 27 Suykens, Johan A. K. 24 Anthony, Martin H. G. 21 Zhou, Dingxuan 20 Sugiyama, Masashi 19 Tian, Yingjie 18 Pardalos, Panos M. 18 Ratsaby, Joel 16 Hwang, Changha 16 Li, Luoqing 16 Sun, Hongwei 16 Trafalis, Theodore B. 15 Chen, Dirong 15 Liu, Yufeng 14 Wu, Qiang 13 Carrizosa, Emilio 13 Chung, Fu-Lai 13 Deng, Naiyang 13 Lugosi, Gábor 13 Sanguineti, Marcello 13 Shi, Yong 13 Wang, Shitong 12 Chen, Hong 12 Gaudioso, Manlio 12 Kanamori, Takafumi 12 Mangasarian, Olvi L. 12 Tong, Hongzhi 11 Alquier, Pierre 11 Christmann, Andreas 11 Devroye, Luc P. J. A. 11 Peng, Xinjun 10 Gnecco, Giorgio 10 Shao, Yuanhai 9 Bartlett, Peter L. 9 De Moor, Bart L. R. 9 Dougherty, Edward R. 9 Ha, Minghu 9 Hanneke, Steve 9 Haussler, David 9 Matoušek, Jiří 9 Príncipe, José Carlos 9 Shim, Jooyong 9 Xiang, Dao-Hong 9 Xu, Zongben 9 Zou, Bin 8 Apolloni, Bruno 8 Astorino, Annabella 8 Biau, Gérard 8 Cao, Feilong 8 Chen, Songcan 8 Guarracino, Mario Rosario 8 Long, Philip M. 8 Schölkopf, Bernhard 8 Steinwart, Ingo 8 Takeda, Akiko 8 Tsybakov, Alexandre B. 8 Xu, Yuesheng 7 Calafiore, Giuseppe Carlo 7 Chakraborty, Sounak 7 García-Gonzalo, Esperanza 7 Hayat, Maqsood 7 Kolchinskiĭ, Vladimir I’ich 7 Lai, Kinkeung 7 Lecué, Guillaume 7 Maldonado, Sebastián 7 Matías, José M. 7 Mohri, Mehryar 7 Nobel, Andrew B. 7 Shawe-Taylor, John 7 Sheng, Baohuai 7 Taboada, Javier 7 Zhang, Haizhang 7 Zhang, Li 7 Zhou, Weida 7 Zopounidis, Constantin 6 Bai, Yanqin 6 Bertsimas, Dimitris John 6 Chandra, Suresh 6 Cherkassky, Vladimir S. 6 Hao, Peiyi 6 Härdle, Wolfgang Karl 6 Hong, Dug Hun 6 Hu, Qinghua 6 Hu, Ting 6 Kearns, Michael Justin 6 Khachay, Mikhail Yur’evich 6 Lee, Jaewon 6 Lin, Chih-Jen 6 López, Julio E. 6 Loustau, Sébastien 6 Luo, Jian 6 Maass, Wolfgang 6 Marron, James Stephen 6 Martin-Barragan, Belen 6 Massart, Pascal 6 Mendelson, Shahar 6 Palagi, Laura 6 Pedrycz, Witold 6 Peherstorfer, Benjamin 6 Pelckmans, Kristiaan 6 Pillonetto, Gianluigi ...and 6,399 more Authors
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#### Cited in 425 Serials

 280 Pattern Recognition 118 Neural Networks 97 Information Sciences 91 Machine Learning 78 Neural Computation 74 European Journal of Operational Research 69 Computational Statistics and Data Analysis 66 Journal of Theoretical Biology 55 Theoretical Computer Science 52 The Annals of Statistics 50 Mathematical Problems in Engineering 49 Applied Mathematics and Computation 44 Discrete Applied Mathematics 38 Fuzzy Sets and Systems 36 Automatica 36 Journal of Computer and System Sciences 32 Computational & Mathematical Methods in Medicine 30 Journal of Machine Learning Research (JMLR) 29 Annals of Operations Research 29 Computational Optimization and Applications 29 Electronic Journal of Statistics 27 Soft Computing 27 International Journal of Wavelets, Multiresolution and Information Processing 26 Statistics & Probability Letters 26 Discrete & Computational Geometry 25 Artificial Intelligence 25 Journal of Statistical Planning and Inference 25 Journal of Complexity 24 Optimization Methods & Software 23 Journal of Computational and Applied Mathematics 23 Journal of Multivariate Analysis 23 Computers & Operations Research 22 Computers & Mathematics with Applications 22 Statistical Analysis and Data Mining 21 Cybernetics and Systems Analysis 20 Applied Mathematical Modelling 19 Automation and Remote Control 19 Advances in Computational Mathematics 19 Computational Biology and Chemistry 19 Advances in Data Analysis and Classification. ADAC 18 Signal Processing 18 Computational Statistics 18 Applied and Computational Harmonic Analysis 17 Journal of Optimization Theory and Applications 17 Information and Computation 16 International Journal of Approximate Reasoning 16 Journal of Global Optimization 16 Mathematical Programming. Series A. Series B 16 The Annals of Applied Statistics 15 Information Processing Letters 15 Annals of Mathematics and Artificial Intelligence 15 International Journal of Applied Mathematics and Computer Science 15 Algorithms 14 Computer Methods in Applied Mechanics and Engineering 14 International Journal of General Systems 14 Journal of Computational Physics 14 Mathematical and Computer Modelling 14 International Journal of Computer Mathematics 14 Bernoulli 14 Abstract and Applied Analysis 14 Optimization Letters 13 Journal of the Franklin Institute 13 Analysis and Applications (Singapore) 12 Communications in Statistics. Theory and Methods 12 Computational Management Science 11 Discrete Mathematics 11 Journal of Combinatorial Theory. Series A 11 Statistical Science 11 Communications in Statistics. Simulation and Computation 11 International Journal of Computer Vision 11 Data Mining and Knowledge Discovery 11 Journal of Applied Statistics 11 Quantitative Finance 10 International Journal of Systems Science 10 Journal of Classification 10 International Journal of Intelligent Systems 10 Test 10 PAA. Pattern Analysis and Applications 10 Journal of Systems Science and Complexity 10 Journal of Zhejiang University. Science A 10 Statistics and Computing 9 Mathematical Biosciences 9 Journal of Approximation Theory 9 Systems & Control Letters 9 Journal of Mathematical Imaging and Vision 9 Wuhan University Journal of Natural Sciences (WUJNS) 8 Journal of Mathematical Analysis and Applications 8 Biometrics 8 Journal of the American Statistical Association 8 Algorithmica 8 Computational Geometry 8 SIAM Journal on Optimization 8 European Journal of Control 8 Journal of the Korean Statistical Society 7 Biological Cybernetics 7 Mathematics and Computers in Simulation 7 Combinatorica 7 Probability Theory and Related Fields 7 New Generation Computing 7 Journal of Nonparametric Statistics ...and 325 more Serials
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#### Cited in 55 Fields

 1,958 Computer science (68-XX) 1,244 Statistics (62-XX) 470 Operations research, mathematical programming (90-XX) 305 Biology and other natural sciences (92-XX) 274 Numerical analysis (65-XX) 187 Systems theory; control (93-XX) 159 Probability theory and stochastic processes (60-XX) 156 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 127 Information and communication theory, circuits (94-XX) 102 Combinatorics (05-XX) 62 Functional analysis (46-XX) 38 Approximations and expansions (41-XX) 34 Convex and discrete geometry (52-XX) 34 Mechanics of deformable solids (74-XX) 31 Mathematical logic and foundations (03-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 24 Dynamical systems and ergodic theory (37-XX) 24 Geophysics (86-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 17 Partial differential equations (35-XX) 16 Quantum theory (81-XX) 15 Operator theory (47-XX) 14 Fluid mechanics (76-XX) 12 Order, lattices, ordered algebraic structures (06-XX) 10 Measure and integration (28-XX) 9 Ordinary differential equations (34-XX) 9 Integral equations (45-XX) 9 Optics, electromagnetic theory (78-XX) 7 Number theory (11-XX) 7 Statistical mechanics, structure of matter (82-XX) 5 Differential geometry (53-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Commutative algebra (13-XX) 4 General topology (54-XX) 4 Algebraic topology (55-XX) 4 Relativity and gravitational theory (83-XX) 3 Topological groups, Lie groups (22-XX) 3 Real functions (26-XX) 3 Functions of a complex variable (30-XX) 3 Geometry (51-XX) 3 Mechanics of particles and systems (70-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Group theory and generalizations (20-XX) 2 Special functions (33-XX) 2 Difference and functional equations (39-XX) 2 Global analysis, analysis on manifolds (58-XX) 1 Field theory and polynomials (12-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Manifolds and cell complexes (57-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)

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