Neural nets learning as an inverse problem

Věra Pohlová

Pokroky matematiky, fyziky a astronomie (2004)

  • Volume: 49, Issue: 3, page 218-225
  • ISSN: 0032-2423

How to cite

top

Pohlová, Věra. "Učení neuronových sítí jako inverzní úloha." Pokroky matematiky, fyziky a astronomie 49.3 (2004): 218-225. <http://eudml.org/doc/196545>.

@article{Pohlová2004,
author = {Pohlová, Věra},
journal = {Pokroky matematiky, fyziky a astronomie},
keywords = {machine learning; reproducing kernel; Hilbert space; machine learning; reproducing kernel; Hilbert space},
language = {cze},
number = {3},
pages = {218-225},
publisher = {Jednota českých matematiků a fyziků},
title = {Učení neuronových sítí jako inverzní úloha},
url = {http://eudml.org/doc/196545},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Pohlová, Věra
TI - Učení neuronových sítí jako inverzní úloha
JO - Pokroky matematiky, fyziky a astronomie
PY - 2004
PB - Jednota českých matematiků a fyziků
VL - 49
IS - 3
SP - 218
EP - 225
LA - cze
KW - machine learning; reproducing kernel; Hilbert space; machine learning; reproducing kernel; Hilbert space
UR - http://eudml.org/doc/196545
ER -

References

top
  1. Aronszajn, N., 10.1090/S0002-9947-1950-0051437-7, Trans. Amer. Math. Soc. 68 (1950), 33–404. (1950) Zbl0037.20701MR0051437DOI10.1090/S0002-9947-1950-0051437-7
  2. Berg, C., Christensen, J. P. R., Ressel, P., Harmonic Analysis on Semigroups, Springer-Verlag, New York 1984. (1984) Zbl0619.43001MR0747302
  3. Bertero, M., Linear inverse and ill-posed problems, Advances in Electronics and Electron Physics 75 (1989), 1–120. (1989) 
  4. Bjorck, A., Numerical methods for least squares problem, SIAM 1996. (1996) Zbl0847.65023MR1386889
  5. Cucker, F., Smale, S., 10.1090/S0273-0979-01-00923-5, Bull. Amer. Math. Soc. 39 (2001), 1–49. (2001) Zbl0983.68162MR1864085DOI10.1090/S0273-0979-01-00923-5
  6. Friedman, A., Modern Analysis, Dover, New York 1982. (1982) Zbl0557.46001MR0663003
  7. Girosi, F., 10.1162/089976698300017269, Neural Computation 10 (1998), 1455–1480 (AI Memo No 1606, MIT). (1998) DOI10.1162/089976698300017269
  8. Groetch, C. W., Generalized Inverses of Linear Operators, Dekker, New York 1977. (1977) 
  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. (2003) 
  10. Kůrková, V., Learning from data as an inverse problem, In Proc. of COMPSTAT 2004 (J. Antoch, ed.), Physica-Verlag, Heidelberg, 1377–1384. (2004) Zbl1265.68146MR2173152
  11. Kůrková, V., Sanguineti, M., Error estimates for approximate optimization by the extended Ritz method, SIAM J. Optim. (to appear). Zbl1074.49008MR2144176
  12. Kůrková, V., Sanguineti, M., Learning with generalization capability by kernel methods with bounded complexity, J. Compl. (to appear). Zbl1216.68135MR2138445
  13. Moore, E. H., Abstract, Bulletin AMS 26 (1920), 394–395. (1920) 
  14. Narcowich, F. J., Sivakumar, N., Ward, J. D., 10.1006/jmaa.1994.1311, J. Math. Anal. Appl. 186 (1994), 457–485. (1994) Zbl0813.65005MR1293005DOI10.1006/jmaa.1994.1311
  15. Parzen, E., 10.1214/aoms/1177704840, Annals Math. Statistics 32 (1966), 951–989. (1966) Zbl0107.13801MR0143315DOI10.1214/aoms/1177704840
  16. Penrose, R., A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 52 (1955), 406–413. (1955) Zbl0065.24603MR0069793
  17. Poggio, T., Girosi, F., Networks for approximation and learning, Proc. IEEE 78 (1990), 1481–1497. (1990) Zbl1226.92005
  18. Poggio, T., Smale, S., The mathematics of learning: dealing with data, Notices Amer. Math. Soc. 50 (2003), 536–544. (2003) Zbl1083.68100MR1968413
  19. Sejnowski, T. J., Rosenberg, C., Parallel networks that learn to pronounce English text, Complex Systems 1 (1987), 145–168. (1987) Zbl0655.68107
  20. Tichonov, A. N., Arsenin, V. Y., Solutions of Ill-posed Problems, W. H. Winston, Washington, D. C. 1977. (1977) 
  21. Wahba, G., Splines Models for Observational Data, SIAM, Philadelphia 1990. (1990) Zbl0813.62001MR1045442
  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. (1995) 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.