| Title:
|
Učení neuronových sítí jako inverzní úloha (Czech) |
| Title:
|
Neural nets learning as an inverse problem (English) |
| Author:
|
Kůrková, Věra |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
218-225 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
machine learning |
| Keyword:
|
reproducing kernel |
| Keyword:
|
Hilbert space |
| MSC:
|
46E22 |
| MSC:
|
47B32 |
| MSC:
|
65J22 |
| MSC:
|
68T05 |
| MSC:
|
82N32 |
| idZBL:
|
Zbl 1265.68146 |
| . |
| Date available:
|
2010-12-11T20:37:23Z |
| Last updated:
|
2015-11-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141231 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[3] Bertero, M.: Linear inverse and ill-posed problems.Advances in Electronics and Electron Physics 75 (1989), 1–120. |
| Reference:
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[4] Bjorck, A.: Numerical methods for least squares problem.SIAM 1996. MR 1386889 |
| Reference:
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| Reference:
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[6] Friedman, A.: Modern Analysis.Dover, New York 1982. Zbl 0557.46001, MR 0663003 |
| Reference:
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| Reference:
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[8] Groetch, C. W.: Generalized Inverses of Linear Operators.Dekker, New York 1977. |
| Reference:
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[9] Kůrková, V.: High-dimensional approximation by neural networks.Chapter 4 in Advances in Learning Theory: Methods, Models and Applications (J. Stuykens et al., ed.) (2003), 69–88. IOS Press, Amsterdam. |
| Reference:
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[10] Kůrková, V.: Learning from data as an inverse problem.In Proc. of COMPSTAT 2004 (J. Antoch, ed.), Physica-Verlag, Heidelberg, 1377–1384. MR 2173152 |
| Reference:
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[11] Kůrková, V., Sanguineti, M.: Error estimates for approximate optimization by the extended Ritz method.SIAM J. Optim. (to appear). MR 2144176 |
| Reference:
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[12] Kůrková, V., Sanguineti, M.: Learning with generalization capability by kernel methods with bounded complexity.J. Compl. (to appear). MR 2138445 |
| Reference:
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[13] Moore, E. H.: Abstract.Bulletin AMS 26 (1920), 394–395. |
| Reference:
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[14] Narcowich, F. J., Sivakumar, N., Ward, J. D.: On condition numbers associated with radial-function interpolation.J. Math. Anal. Appl. 186 (1994), 457–485. Zbl 0813.65005, MR 1293005, 10.1006/jmaa.1994.1311 |
| Reference:
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[15] Parzen, E.: An approach to time series analysis.Annals Math. Statistics 32 (1966), 951–989. MR 0143315, 10.1214/aoms/1177704840 |
| Reference:
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[16] Penrose, R.: A generalized inverse for matrices.Proc. Cambridge Philos. Soc. 52 (1955), 406–413. Zbl 0065.24603, MR 0069793 |
| Reference:
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[17] Poggio, T., Girosi, F.: Networks for approximation and learning.Proc. IEEE 78 (1990), 1481–1497. |
| Reference:
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[18] Poggio, T., Smale, S.: The mathematics of learning: dealing with data.Notices Amer. Math. Soc. 50 (2003), 536–544. Zbl 1083.68100, MR 1968413 |
| Reference:
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[19] Sejnowski, T. J., Rosenberg, C.: Parallel networks that learn to pronounce English text.Complex Systems 1 (1987), 145–168. Zbl 0655.68107 |
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[20] Tichonov, A. N., Arsenin, V. Y.: Solutions of Ill-posed Problems.W. H. Winston, Washington, D. C. 1977. |
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| Reference:
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[22] Werbos, P. J.: Backpropagation: Basics and New Developments.The Handbook of Brain Theory and Neural Networks (M. Arbib, ed.), 134–139. MIT Press, Cambridge 1995. |
| . |
