A fast, consistent kernel two-sample test

Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

Volumn , Issue , 2009, Pages 673-681

  Gretton, Arthur ^a   Fukumizu, Kenji ^b   Harchaoui, Zaid ^a   Sriperumbudur, Bharath K ^c  

^a CARNEGIE MELLON UNIVERSITY   (United States)

^b INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SAMPLING; STATISTICAL TESTS;

DIFFERENT DISTRIBUTIONS; EMBEDDINGS; FINITE SAMPLES; NULL DISTRIBUTION; PROBABILITY MEASURES; PROBABILITY: DISTRIBUTIONS; REPRODUCING KERNEL HILBERT SPACES; TWO-SAMPLE TESTS; WEIGHTED SUM; ZERO IF;

PROBABILITY DISTRIBUTIONS;

EID: 80053164096     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (32)

1. N. Anderson, P. Hall, and D. Titterington. Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates. Journal of Multivariate Analysis, 50:41-54, 1994.
2. F. R. Bach and M. I. Jordan. Kernel independent component analysis. J. Mach. Learn. Res., 3:1-48, 2002.
3. C. Baker. Joint measures and cross-covariance operators. Transactions of the American Mathematical Society, 186:273-289, 1973.
4. A. Berlinet and C. Thomas-Agnan. Reproducing Kernel Hilbert Spaces in Probability and Statistics. Springer-Verlag, Berlin, 2003.
5. Rajendra Bhatia and Ludwig Elsner. The Hoffman-Wielandt inequality in infinite dimensions. Proceedings of Indian Academy of Science (Mathematical Sciences), 104(3):483-494, 1994.
6. 1-test statistic of homogeneity. IEEE Transactions on Information Theory, 51(11):3965-3973, 2005.
7. G. Blanchard, O. Bousquet, and L. Zwald. Statistical properties of kernel principal component analysis. Machine Learning, 66:259-294, 2007.
8. K. M. Borgwardt, A. Gretton, M. J. Rasch, H.-P. Kriegel, B. Schölkopf, and A. J. Smola. Integrating structured biological data by kernel maximum mean discrepancy. Bioinformatics (ISMB), 22(14):e49- e57, 2006.
9. J. Friedman and L. Rafsky. Multivariate generalizations of the Wald-Wolfowitz and Smirnov two-sample tests. The Annals of Statistics, 7(4):697-717, 1979.
10. K. Fukumizu, F. R. Bach, and M. I. Jordan. Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces. J. Mach. Learn. Res., 5:73-99, 2004.
11. K. Fukumizu, A. Gretton, X. Sun, and B. Schölkopf. Kernel measures of conditional dependence. In NIPS 20, pages 489-496, 2008.
12. K. Fukumizu, B. Sriperumbudur, A. Gretton, and B. Schölkopf. Characteristic kernels on groups and semigroups. In NIPS 21, pages 473-480, 2009.
13. G. Golub and Q. Ye. An inverse free preconditioned krylov subspace method for symmetric generalized eigenvalue problems. SIAM Journal on Scientific Computing, 24:312-334, 2002.
14. A. Gretton, K. Borgwardt, M. Rasch, B. Schölkopf, and A. Smola. A kernel method for the two-sample-problem. In NIPS 19, pages 513-520, 2007.
15. A. Gretton, K. Fukumizu, C.-H. Teo, L. Song, B. Schölkopf, and A. Smola. A kernel statistical test of independence. In NIPS 20, pages 585-592, 2008.
16. G. R. Grimmet and D. R. Stirzaker. Probability and Random Processes. Oxford University Press, Oxford, third edition, 2001.
17. P. Hall and N. Tajvidi. Permutation tests for equality of distributions in high-dimensional settings. Biometrika, 89(2):359-374, 2002.
18. Z. Harchaoui, F. Bach, and E. Moulines. Testing for homogeneity with kernel fisher discriminant analysis. In NIPS 20, pages 609-616. 2008. (long version: arXiv:0804.1026v1).
19. M. Hein and O. Bousquet. Kernels, associated structures, and generalizations. Technical Report 127, Max Planck Institute for Biological Cybernetics, 2004.
20. N. L. Johnson, S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions. Volume 1 (Second Edition). John Wiley and Sons, 1994.
21. E. Lehmann and J. Romano. Testing Statistical Hypothesis (3rd ed.). Wiley, New York, 2005.
22. C. Leslie, E. Eskin, and W. S. Noble. The spectrum kernel: A string kernel for SVM protein classification. In Proceedings of the Pacific Symposium on Biocomputing, pages 564-575, 2002.
23. A. S. Markus. The eigen- and singular values of the sum and product of linear operators. Russian Mathematical Surveys, 19(4):93-123, 1964.
24. M. Rasch, A. Gretton, Y. Murayama, W. Maass, and N. K. Logothetis. Predicting spiking activity from local field potentials. Journal of Neurophysiology, 99:1461-1476, 2008.
25. B. Schölkopf and A. Smola. Learning with Kernels. MIT Press, Cambridge, MA, 2002.
26. B. Schölkopf, A. J. Smola, and K.-R. Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10:1299-1319, 1998.
27. J. Shawe-Taylor, C. Williams, N. Cristianini, and J. Kandola. On the eigenspectrum of the Gram matrix and the generalisation error of kernel PCA. IEEE Trans. Inf. Theory, 51(7):2510-2522, 2005.
28. A. J. Smola, A. Gretton, L. Song, and B. Schölkopf. A Hilbert space embedding for distributions. In ALT 18, pages 13-31, 2007.
29. B. Sriperumbudur, A. Gretton, K. Fukumizu, G. Lanckriet, and B. Schölkopf. Injective hilbert space embeddings of probability measures. In COLT 21, pages 111-122, 2008.
30. C. H. Teo and S. V. N. Vishwanathan. Fast and space efficient string kernels using suffix arrays. In ICML, pages 929-936, 2006.
31. J. E. Wilkins. A note on skewness and kurtosis. Ann. Math. Stat., 15(3):333-335, 1944.
32. G. Zech and B. Aslan. A multivariate two-sample test based on the concept of minimum energy. In PHYSTAT, pages 97-100, 2003.