-
2
-
-
0027599793
-
Universal approximation bounds for superpositions of a sigmoidal function
-
Barron, A.R.: Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. on Information Theory 39, 930-945 (1993)
-
(1993)
IEEE Trans. on Information Theory
, vol.39
, pp. 930-945
-
-
Barron, A.R.1
-
3
-
-
85012688561
-
-
Princeton University Press, Princeton
-
Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)
-
(1957)
Dynamic Programming
-
-
Bellman, R.1
-
6
-
-
0027602489
-
Hinging hyperplanes for regression, classification and function approximation
-
Breiman, L.: Hinging hyperplanes for regression, classification and function approximation. IEEE Trans. Inform. Theory 39(3), 999-1013 (1993)
-
(1993)
IEEE Trans. Inform. Theory
, vol.39
, Issue.3
, pp. 999-1013
-
-
Breiman, L.1
-
9
-
-
21844505259
-
Neural networks for localized approximation
-
Chui, C.K., Li, X., Mhaskar, H.N.: Neural networks for localized approximation. Math. of Computation 63, 607-623 (1994)
-
(1994)
Math. of Computation
, vol.63
, pp. 607-623
-
-
Chui, C.K.1
Li, X.2
Mhaskar, H.N.3
-
11
-
-
0024861871
-
Approximation by superpositions of a sigmoidal function
-
Cybenko, G.: Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals, and Systems 2, 303-314 (1989)
-
(1989)
Mathematics of Control, Signals, and Systems
, vol.2
, pp. 303-314
-
-
Cybenko, G.1
-
12
-
-
0027833246
-
Rate of approximation results motivated by robust neural network learning
-
ACM, New York
-
Darken, C., Donahue, M., Gurvits, L., Sontag, E.: Rate of approximation results motivated by robust neural network learning. In: Proc. Sixth Annual ACM Conf. on Computational Learning Theory, pp. 303-309. ACM, New York (1993)
-
(1993)
Proc. Sixth Annual ACM Conf. on Computational Learning Theory
, pp. 303-309
-
-
Darken, C.1
Donahue, M.2
Gurvits, L.3
Sontag, E.4
-
13
-
-
0000910028
-
Optimal nonlinear approximation
-
DeVore, R.A., Howard, R., Micchelli, C.: Optimal nonlinear approximation. Manuscripta Mathematica 63, 469-478 (1989)
-
(1989)
Manuscripta Mathematica
, vol.63
, pp. 469-478
-
-
DeVore, R.A.1
Howard, R.2
Micchelli, C.3
-
14
-
-
0031531584
-
Rates of convex approximation in non-Hilbert spaces
-
Donahue, M., Gurvits, L., Darken, C., Sontag, E.: Rates of convex approximation in non-Hilbert spaces. Constructive Approximation 13, 187-220 (1997)
-
(1997)
Constructive Approximation
, vol.13
, pp. 187-220
-
-
Donahue, M.1
Gurvits, L.2
Darken, C.3
Sontag, E.4
-
15
-
-
0003085388
-
Rates of convergence for Radial Basis Functions and neural networks
-
In: Mammone, R.J. (ed.), Chapman & Hall
-
Girosi, F., Anzellotti, G.: Rates of convergence for Radial Basis Functions and neural networks. In: Mammone, R.J. (ed.) Artificial Neural Networks for Speech and Vision, pp. 97-113. Chapman & Hall (1993)
-
(1993)
Artificial Neural Networks for Speech and Vision
, pp. 97-113
-
-
Girosi, F.1
Anzellotti, G.2
-
16
-
-
0024991997
-
Networks and the best approximation property
-
Girosi, F., Poggio, T.: Networks and the best approximation property. Biological Cybernetics 63, 169-176 (1990)
-
(1990)
Biological Cybernetics
, vol.63
, pp. 169-176
-
-
Girosi, F.1
Poggio, T.2
-
18
-
-
77949570561
-
Estimates of variation with respect to a set and applications to optimization problems
-
Gnecco, G., Sanguineti, M.: Estimates of variation with respect to a set and applications to optimization problems. J. of Optimization Theory and Applications 145, 53-75 (2010)
-
(2010)
J. of Optimization Theory and Applications
, vol.145
, pp. 53-75
-
-
Gnecco, G.1
Sanguineti, M.2
-
19
-
-
78650896759
-
On a variational norm tailored to variable-basis approximation schemes
-
Gnecco, G., Sanguineti, M.: On a variational norm tailored to variable-basis approximation schemes. IEEE Trans. on Information Theory 57, 549-558 (2011)
-
(2011)
IEEE Trans. on Information Theory
, vol.57
, pp. 549-558
-
-
Gnecco, G.1
Sanguineti, M.2
-
20
-
-
32944458952
-
On the exponential convergence of matching pursuits in quasi-incoherent dictionaries
-
Gribonval, R., Vandergheynst, P.: On the exponential convergence of matching pursuits in quasi-incoherent dictionaries. IEEE Trans. on Information Theory 52, 255-261 (2006)
-
(2006)
IEEE Trans. on Information Theory
, vol.52
, pp. 255-261
-
-
Gribonval, R.1
Vandergheynst, P.2
-
22
-
-
0001683814
-
Layered neural networks with Gaussian hidden units as universal approximations
-
Hartman, E.J., Keeler, J.D., Kowalski, J.M.: Layered neural networks with Gaussian hidden units as universal approximations. Neural Computation 2, 210-215 (1990)
-
(1990)
Neural Computation
, vol.2
, pp. 210-215
-
-
Hartman, E.J.1
Keeler, J.D.2
Kowalski, J.M.3
-
24
-
-
0025627940
-
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks
-
Hornik, K., Stinchcombe, M., White, H.: Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks 3, 551-560 (1990)
-
(1990)
Neural Networks
, vol.3
, pp. 551-560
-
-
Hornik, K.1
Stinchcombe, M.2
White, H.3
-
25
-
-
0025799121
-
Representation of functions by superpositions of a step or sigmoidal function and their applications to neural network theory
-
Ito, Y.: Representation of functions by superpositions of a step or sigmoidal function and their applications to neural network theory. Neural Networks 4, 385-394 (1991)
-
(1991)
Neural Networks
, vol.4
, pp. 385-394
-
-
Ito, Y.1
-
26
-
-
0001929506
-
Finite mapping by neural networks and truth functions
-
Ito, Y.: Finite mapping by neural networks and truth functions. Mathematical Scientist 17, 69-77 (1992)
-
(1992)
Mathematical Scientist
, vol.17
, pp. 69-77
-
-
Ito, Y.1
-
27
-
-
0000796112
-
A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training
-
Jones, L.K.: A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training. Annals of Statistics 20, 608-613 (1992)
-
(1992)
Annals of Statistics
, vol.20
, pp. 608-613
-
-
Jones, L.K.1
-
28
-
-
0029482971
-
Nonlinear black-box models in system identification: Mathematical foundations
-
Juditsky, A., Hjalmarsson, H., Benveniste, A., Delyon, B., Ljung, L., Sjöberg, J., Zhang, Q.: Nonlinear black-box models in system identification: Mathematical foundations. Automatica 31, 1725-1750 (1995)
-
(1995)
Automatica
, vol.31
, pp. 1725-1750
-
-
Juditsky, A.1
Hjalmarsson, H.2
Benveniste, A.3
Delyon, B.4
Ljung, L.5
Sjöberg, J.6
Zhang, Q.7
-
30
-
-
56949103612
-
Complexity of Gaussian radial basis networks approximating smooth functions
-
Kainen, P.C., Kůrková, V., Sanguineti, M.: Complexity of Gaussian radial basis networks approximating smooth functions. J. of Complexity 25, 63-74 (2009)
-
(2009)
J. of Complexity
, vol.25
, pp. 63-74
-
-
Kainen, P.C.1
Kůrková, V.2
Sanguineti, M.3
-
31
-
-
84856932727
-
Dependence of Computational Models on Input Dimension: Tractability of Approximation and Optimization Tasks
-
Kainen, P.C., Kurkova, V., Sanguineti, M.: Dependence of Computational Models on Input Dimension: Tractability of Approximation and Optimization Tasks. IEEE Transactions on Information Theory 58, 1203-1214 (2012)
-
(2012)
IEEE Transactions on Information Theory
, vol.58
, pp. 1203-1214
-
-
Kainen, P.C.1
Kurkova, V.2
Sanguineti, M.3
-
32
-
-
0008241587
-
Geometry and topology of continuous best and near best approximations
-
Kainen, P.C., Kůrková, V., Vogt, A.: Geometry and topology of continuous best and near best approximations. J. of Approximation Theory 105, 252-262 (2000)
-
(2000)
J. of Approximation Theory
, vol.105
, pp. 252-262
-
-
Kainen, P.C.1
Kůrková, V.2
Vogt, A.3
-
33
-
-
0043289787
-
Continuity of approximation by neural networks in Lp-spaces
-
Kainen, P.C., Kůrková, V., Vogt, A.: Continuity of approximation by neural networks in Lp-spaces. Annals of Operational Research 101, 143-147 (2001)
-
(2001)
Annals of Operational Research
, vol.101
, pp. 143-147
-
-
Kainen, P.C.1
Kůrková, V.2
Vogt, A.3
-
34
-
-
0038009873
-
Best approximation by linear combinations of characteristic functions of half-spaces
-
Kainen, P.C., Kůrková, V., Vogt, A.: Best approximation by linear combinations of characteristic functions of half-spaces. J. of Approximation Theory 122, 151-159 (2003)
-
(2003)
J. of Approximation Theory
, vol.122
, pp. 151-159
-
-
Kainen, P.C.1
Kůrková, V.2
Vogt, A.3
-
35
-
-
34447641642
-
A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves
-
Kainen, P.C., Kůrková, V., Vogt, A.: A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves. J. of Approximation Theory 147, 1-10 (2007)
-
(2007)
J. of Approximation Theory
, vol.147
, pp. 1-10
-
-
Kainen, P.C.1
Kůrková, V.2
Vogt, A.3
-
36
-
-
0003026625
-
Big omicron and big omega and big theta
-
Knuth, D.E.: Big omicron and big omega and big theta. SIGACT News 8, 18-24 (1976)
-
(1976)
SIGACT News
, vol.8
, pp. 18-24
-
-
Knuth, D.E.1
-
37
-
-
0026627415
-
Kolmogorov's theorem and multilayer neural networks
-
Kůrková, V.: Kolmogorov's theorem and multilayer neural networks. Neural Networks 5, 501-506 (1992)
-
(1992)
Neural Networks
, vol.5
, pp. 501-506
-
-
Kůrková, V.1
-
38
-
-
0028790449
-
Approximation of functions by perceptron networks with bounded number of hidden units
-
Kůrková, V.: Approximation of functions by perceptron networks with bounded number of hidden units. Neural Networks 8, 745-750 (1995)
-
(1995)
Neural Networks
, vol.8
, pp. 745-750
-
-
Kůrková, V.1
-
39
-
-
0000025506
-
Dimension-independent rates of approximation by neural networks
-
In: Warwick, K., Kárný, M. (eds.), Birkhäuser, Boston, MA
-
Kůrková, V.: Dimension-independent rates of approximation by neural networks. In: Warwick, K., Kárný, M. (eds.) Computer-Intensive Methods in Control and Signal Processing. The Curse of Dimensionality, Birkhäuser, Boston, MA, pp. 261-270 (1997)
-
(1997)
Computer-Intensive Methods in Control and Signal Processing. The Curse of Dimensionality
, pp. 261-270
-
-
Kůrková, V.1
-
40
-
-
0002806299
-
Incremental approximation by neural networks
-
In: Warwick, K., Kárný, M., Kůrková, V. (eds.), Springer, London
-
Kůrková, V.: Incremental approximation by neural networks. In: Warwick, K., Kárný, M., Kůrková, V. (eds.) Complexity: Neural Network Approach, pp. 177-188. Springer, London (1998)
-
(1998)
Complexity: Neural Network Approach
, pp. 177-188
-
-
Kůrková, V.1
-
41
-
-
4043167595
-
High-dimensional approximation and optimization by neural networks
-
In: Suykens, J., et al. (eds.), ch. 4, IOS Press, Amsterdam
-
Kůrková, V.: High-dimensional approximation and optimization by neural networks. In: Suykens, J., et al. (eds.) Advances in Learning Theory: Methods, Models and Applications, ch. 4, pp. 69-88. IOS Press, Amsterdam (2003)
-
(2003)
Advances in Learning Theory: Methods, Models and Applications
, pp. 69-88
-
-
Kůrková, V.1
-
42
-
-
37748999976
-
Minimization of error functionals over perceptron networks
-
Kůrková, V.: Minimization of error functionals over perceptron networks. Neural Computation 20, 252-270 (2008)
-
(2008)
Neural Computation
, vol.20
, pp. 252-270
-
-
Kůrková, V.1
-
43
-
-
0343118761
-
Estimates of the number of hidden units and variation with respect to half-spaces
-
Kůrková, V., Kainen, P.C., Kreinovich, V.: Estimates of the number of hidden units and variation with respect to half-spaces. Neural Networks 10, 1061-1068 (1997)
-
(1997)
Neural Networks
, vol.10
, pp. 1061-1068
-
-
Kůrková, V.1
Kainen, P.C.2
Kreinovich, V.3
-
44
-
-
24544481301
-
Uniqueness of functional representations by Gaussian basis function networks
-
Springer, London
-
Kůrková, V., Neruda, R.: Uniqueness of functional representations by Gaussian basis function networks. In: Proceedings of ICANN 1994, pp. 471-474. Springer, London (1994)
-
(1994)
Proceedings of ICANN 1994
, pp. 471-474
-
-
Kůrková, V.1
Neruda, R.2
-
45
-
-
0035443484
-
Bounds on rates of variable-basis and neuralnetwork approximation
-
Kůrková, V., Sanguineti, M.: Bounds on rates of variable-basis and neuralnetwork approximation. IEEE Trans. on Information Theory 47, 2659-2665 (2001)
-
(2001)
IEEE Trans. on Information Theory
, vol.47
, pp. 2659-2665
-
-
Kůrková, V.1
Sanguineti, M.2
-
46
-
-
0036165028
-
Comparison of worst case errors in linear and neural network approximation
-
Kůrková, V., Sanguineti, M.: Comparison of worst case errors in linear and neural network approximation. IEEE Trans. on Information Theory 48, 264-275 (2002)
-
(2002)
IEEE Trans. on Information Theory
, vol.48
, pp. 264-275
-
-
Kůrková, V.1
Sanguineti, M.2
-
47
-
-
18744392546
-
Error estimates for approximate optimization by the extended Ritz method
-
Kůrková, V., Sanguineti, M.: Error estimates for approximate optimization by the extended Ritz method. SIAM J. on Optimization 15, 261-287 (2005)
-
(2005)
SIAM J. on Optimization
, vol.15
, pp. 261-287
-
-
Kůrková, V.1
Sanguineti, M.2
-
48
-
-
18144390163
-
Learning with generalization capability by kernel methods of bounded complexity
-
Kůrková, V., Sanguineti, M.: Learning with generalization capability by kernel methods of bounded complexity. J. of Complexity 21, 350-367 (2005)
-
(2005)
J. of Complexity
, vol.21
, pp. 350-367
-
-
Kůrková, V.1
Sanguineti, M.2
-
49
-
-
34547732358
-
Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets
-
Kůrková, V., Sanguineti, M.: Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets. Discrete Applied Mathematics 155, 1930-1942 (2007)
-
(2007)
Discrete Applied Mathematics
, vol.155
, pp. 1930-1942
-
-
Kůrková, V.1
Sanguineti, M.2
-
50
-
-
61349203972
-
Approximate minimization of the regularized expected error over kernel models
-
Kůrková, V., Sanguineti, M.: Approximate minimization of the regularized expected error over kernel models. Mathematics of Operations Research 33, 747-756 (2008)
-
(2008)
Mathematics of Operations Research
, vol.33
, pp. 747-756
-
-
Kůrková, V.1
Sanguineti, M.2
-
51
-
-
57349097663
-
Geometric upper bounds on rates of variable-basis approximation
-
Kůrková, V., Sanguineti, M.: Geometric upper bounds on rates of variable-basis approximation. IEEE Trans. on Information Theory 54, 5681-5688 (2008)
-
(2008)
IEEE Trans. on Information Theory
, vol.54
, pp. 5681-5688
-
-
Kůrková, V.1
Sanguineti, M.2
-
52
-
-
0032096332
-
Representations and rates of approximation of real-valued Boolean functions by neural networks
-
Kůrková, V., Savický, P., Hlaváčková, K.: Representations and rates of approximation of real-valued Boolean functions by neural networks. Neural Networks 11, 651-659 (1998)
-
(1998)
Neural Networks
, vol.11
, pp. 651-659
-
-
Kůrková, V.1
Savický, P.2
Hlaváčková, K.3
-
53
-
-
0036505609
-
On the geometric convergence of neural approximations
-
Lavretsky, E.: On the geometric convergence of neural approximations. IEEE Trans. on Neural Networks 13, 274-282 (2002)
-
(2002)
IEEE Trans. on Neural Networks
, vol.13
, pp. 274-282
-
-
Lavretsky, E.1
-
54
-
-
0027262895
-
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function
-
Leshno, M., Lin, V.Y., Pinkus, A., Schocken, S.: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Networks 6, 861-867 (1993)
-
(1993)
Neural Networks
, vol.6
, pp. 861-867
-
-
Leshno, M.1
Lin, V.Y.2
Pinkus, A.3
Schocken, S.4
-
55
-
-
0030119952
-
Random approximants and neural networks
-
Makovoz, Y.: Random approximants and neural networks. J. of Approximation Theory 85, 98-109 (1996)
-
(1996)
J. of Approximation Theory
, vol.85
, pp. 98-109
-
-
Makovoz, Y.1
-
57
-
-
3242701678
-
On the tractability of multivariate integration and approximation by neural networks
-
Mhaskar, H.N.: On the tractability of multivariate integration and approximation by neural networks. J. of Complexity 20, 561-590 (2004)
-
(2004)
J. of Complexity
, vol.20
, pp. 561-590
-
-
Mhaskar, H.N.1
-
58
-
-
34250122797
-
Interpolation of scattered data: Distance matrices and conditionally positive definite functions
-
Micchelli, C.A.: Interpolation of scattered data: Distance matrices and conditionally positive definite functions. Constructive Approximation 2, 11-22 (1986)
-
(1986)
Constructive Approximation
, vol.2
, pp. 11-22
-
-
Micchelli, C.A.1
-
59
-
-
0031140389
-
Adaptive control using neural networks and approximate models
-
Narendra, K.S., Mukhopadhyay, S.: Adaptive control using neural networks and approximate models. IEEE Trans. on Neural Networks 8, 475-485 (1997)
-
(1997)
IEEE Trans. on Neural Networks
, vol.8
, pp. 475-485
-
-
Narendra, K.S.1
Mukhopadhyay, S.2
-
60
-
-
0000106040
-
Universal approximation using radial-basis-function networks
-
Park, J., Sandberg, I.W.: Universal approximation using radial-basis-function networks. Neural Computation 3, 246-257 (1991)
-
(1991)
Neural Computation
, vol.3
, pp. 246-257
-
-
Park, J.1
Sandberg, I.W.2
-
61
-
-
0001002401
-
Approximation and radial-basis-function networks
-
Park, J., Sandberg, I.W.: Approximation and radial-basis-function networks. Neural Computation 5, 305-316 (1993)
-
(1993)
Neural Computation
, vol.5
, pp. 305-316
-
-
Park, J.1
Sandberg, I.W.2
-
62
-
-
85011438572
-
Approximation theory of the MLP model in neural networks
-
Pinkus, A.: Approximation theory of the MLP model in neural networks. Acta Numerica 8, 143-195 (1999)
-
(1999)
Acta Numerica
, vol.8
, pp. 143-195
-
-
Pinkus, A.1
-
63
-
-
0003345901
-
Remarques sur un résultat non publié de B
-
Palaiseau, France. École Polytechnique, Centre de Mathématiques
-
Pisier, G.: Remarques sur un résultat non publié de B. Maurey. In: Séminaire d'Analyse Fonctionnelle 1980-1981, Palaiseau, France. École Polytechnique, Centre de Mathématiques, vol. I(12) (1981)
-
(1981)
Maurey. Séminaire d'Analyse Fonctionnelle 1980-1981
, vol.1
, Issue.12
-
-
Pisier, G.1
-
64
-
-
11144273669
-
The perceptron: A probabilistic model for information storage and organization of the brain
-
Rosenblatt, F.: The perceptron: A probabilistic model for information storage and organization of the brain. Psychological Review 65, 386-408 (1958)
-
(1958)
Psychological Review
, vol.65
, pp. 386-408
-
-
Rosenblatt, F.1
-
66
-
-
0000383868
-
Parallel networks that learn to pronounce English text
-
Sejnowski, T.J., Rosenberg, C.: Parallel networks that learn to pronounce English text. Complex Systems 1, 145-168 (1987)
-
(1987)
Complex Systems
, vol.1
, pp. 145-168
-
-
Sejnowski, T.J.1
Rosenberg, C.2
-
68
-
-
0002381070
-
Neural networks for combinatorial optimization: A review of more than a decade of research
-
Smith, K.A.: Neural networks for combinatorial optimization: A review of more than a decade of research. INFORMS J. on Computing 11, 15-34 (1999)
-
(1999)
INFORMS J. on Computing
, vol.11
, pp. 15-34
-
-
Smith, K.A.1
-
69
-
-
0025558060
-
Approximation and learning unknown mappings using multilayer feedforward networks with bounded weights
-
Stinchcombe, M., White, H.: Approximation and learning unknown mappings using multilayer feedforward networks with bounded weights. In: Proc. Int. Joint Conf. on Neural Networks IJCNN 1990, pp. III7-III16 (1990)
-
(1990)
Proc. Int. Joint Conf. on Neural Networks IJCNN 1990
-
-
Stinchcombe, M.1
White, H.2
-
71
-
-
0035702785
-
Complexity of weighted approximation over Rd
-
Wasilkowski, G.W., Woźniakowski, H.: Complexity of weighted approximation over Rd. J. of Complexity 17, 722-740 (2001)
-
(2001)
J. of Complexity
, vol.17
, pp. 722-740
-
-
Wasilkowski, G.W.1
Woźniakowski, H.2
-
72
-
-
38149143192
-
Tractability and strong tractability of linear multivariate problems
-
Woźniakowski, H.: Tractability and strong tractability of linear multivariate problems. J. of Complexity 10, 96-128 (1994)
-
(1994)
J. of Complexity
, vol.10
, pp. 96-128
-
-
Woźniakowski, H.1
-
74
-
-
57349125153
-
-
Springer, London (in preparation)
-
Zoppoli, R., Parisini, T., Sanguineti, M., Baglietto, M.: Neural Approximations for Optimal Control and Decision. Springer, London (in preparation)
-
Neural Approximations for Optimal Control and Decision
-
-
Zoppoli, R.1
Parisini, T.2
Sanguineti, M.3
Baglietto, M.4
-
75
-
-
0036115636
-
Approximating networks and extended Ritz method for the solution of functional optimization problems
-
Zoppoli, R., Sanguineti, M., Parisini, T.: Approximating networks and extended Ritz method for the solution of functional optimization problems. J. of Optimization Theory and Applications 112, 403-439 (2002)
-
(2002)
J. of Optimization Theory and Applications
, vol.112
, pp. 403-439
-
-
Zoppoli, R.1
Sanguineti, M.2
Parisini, T.3
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