On the relation between universality, characteristic kernels and RKHS embedding of measures

Journal of Machine Learning Research

Volumn 9, Issue , 2010, Pages 773-780

  Sriperumbudur, Bharath K ^a   Fukumizu, Kenji ^b   Lanckriet, Gert R G ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACHIEVABILITY; BAYES RISK; BINARY CLASSIFICATION; BOREL MEASURES; HOMOGENEITY TESTING; PROBABILITY MEASURES; REPRODUCING KERNEL HILBERT SPACES; SUFFICIENT CONDITIONS;

SOFTWARE ENGINEERING;

ARTIFICIAL INTELLIGENCE;

EID: 80052200086     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (19)

1. Aronszajn, N. (1950). Theory of reproducing kernels. Trans. Amer. Math. Soc., 68, 337-404.
2. Berg, C., Christensen, J. P. R., & Ressel, P. (1984). Harmonic analysis on semigroups. New York: Spring Verlag.
3. Carmeli, C., Vito, E. D., Toigo, A., & Umanità, V. (2009). Vector valued reproducing kernel Hilbert spaces and universality. Analysis and Applications. To appear.
4. Dunford, N., & Schwartz, J. T. (1958). Linear operators. I: General theory. New York: Wiley-Interscience.
5. Folland, G. B. (1999). Real analysis: Modern techniques and their applications. New York: Wiley-Interscience.
6. Fukumizu, K., Bach, F. R., & Jordan, M. I. (2009a). Kernel dimension reduction in regression. Annals of Statistics, 37, 1871-1905.
7. Fukumizu, K., Gretton, A., Sun, X., & Schölkopf, B. (2008). Kernel measures of conditional dependence. Advances in Neural Information Processing Systems 20 (pp. 489-496). Cambridge, MA: MIT Press.
8. Fukumizu, K., Sriperumbudur, B. K., Gretton, A., & Schölkopf, B. (2009b). Characteristic kernels on groups and semigroups. Advances in Neural Information Processing Systems 21 (pp. 473-480).
9. Gretton, A., Borgwardt, K. M., Rasch, M., Schölkopf, B., & Smola, A. (2007). A kernel method for the two sample problem. Advances in Neural Information Processing Systems 19 (pp. 513-520). MIT Press.
10. Gretton, A., Fukumizu, K., Teo, C.-H., Song, L., Schölkopf, B., & Smola, A. (2008). A kernel statistical test of independence. Advances in Neural Information Processing Systems 20 (pp. 585-592). MIT Press.
11. Hewitt, E. (1950). Linear functionals on spaces of continuous functions. Fundamenta Mathematicae, 37, 161-189.
12. Micchelli, C. A., Xu, Y., & Zhang, H. (2006). Universal kernels. Journal of Machine Learning Research, 7, 2651-2667.
13. Rudin, W. (1991). Functional analysis. USA: McGraw- Hill.
14. Schölkopf, B., & Smola, A. J. (2002). Learning with kernels. Cambridge, MA: MIT Press.
15. Sriperumbudur, B. K., Fukumizu, K., Gretton, A., Lanckriet, G. R. G., & Schölkopf, B. (2009). Kernel choice and classifiability for RKHS embeddings of probability distributions. Advances in Neural Information Processing Systems 22 (pp. 1750-1758). MIT Press.
16. Sriperumbudur, B. K., Gretton, A., Fukumizu, K., Lanckriet, G. R. G., & Schölkopf, B. (2008). Injective Hilbert space embeddings of probability measures. Proc. of the 21st Annual Conference on Learning Theory (pp. 111-122).
17. Steinwart, I. (2001). On the influence of the kernel on the consistency of support vector machines. Journal of Machine Learning Research, 2, 67-93.
18. Steinwart, I., & Christmann, A. (2008). Support vector machines. Springer.
19. Wendland, H. (2005). Scattered data approximation. Cambridge, UK: Cambridge University Press.