nips nips2007 nips2007-192 nips2007-192-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Moulines Eric, Francis R. Bach, Zaïd Harchaoui
Abstract: We propose to investigate test statistics for testing homogeneity based on kernel Fisher discriminant analysis. Asymptotic null distributions under null hypothesis are derived, and consistency against fixed alternatives is assessed. Finally, experimental evidence of the performance of the proposed approach on both artificial and real datasets is provided. 1
[1] D. L. Allen. Hypothesis testing using an L1 -distance bootstrap. The American Statistician, 51(2):145– 150, 1997.
[2] N. H. Anderson, P. Hall, and D. M. Titterington. Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates. Journal of Multivariate Analysis, 50(1):41–54, 1994.
[3] F. Bimbot, J.-F. Bonastre, C. Fredouille, G. Gravier, I. Magrin-Chagnolleau, S. Meignier, T. Merlin, J. Ortega-Garcia, D. Petrovska-Delacretaz, and D. A. Reynolds. A tutorial on text-independent speaker verification. EURASIP, 4:430–51, 2004.
[4] K. Borgwardt, A. Gretton, M. Rasch, H.-P. Kriegel, Sch¨ lkopf, and A. J. Smola. Integrating structured o biological data by kernel maximum mean discrepancy. Bioinformatics, 22(14):49–57, 2006.
[5] H. Brezis. Analyse Fonctionnelle. Masson, 1980.
[6] C. Butucea and K. Tribouley. Nonparametric homogeneity tests. Journal of Statistical Planning and Inference, 136(3):597–639, 2006.
[7] E. Carlstein, H. M¨ ller, and D. Siegmund, editors. Change-point Problems, number 23 in IMS Monou graph. Institute of Mathematical Statistics, Hayward, CA, 1994.
[8] K. Fukumizu, A. Gretton, X. Sunn, and B. Sch¨ lkopf. Kernel measures of conditional dependence. In o Adv. NIPS, 2008.
[9] I. Gohberg, S. Goldberg, and M. A. Kaashoek. Classes of Linear Operators Vol. I. Birkh¨ user, 1990. a
[10] U. Grenander and M. Miller. Pattern Theory: from representation to inference. Oxford Univ. Press, 2007.
[11] A. Gretton, K. Borgwardt, M. Rasch, B. Schoelkopf, and A. Smola. A kernel method for the two-sample problem. In Adv. NIPS, 2006.
[12] P. Hall and C. Heyde. Martingale Limit Theory and Its Application. Academic Press, 1980.
[13] P. Hall and N. Tajvidi. Permutation tests for equality of distributions in high-dimensional settings. Biometrika, 89(2):359–374, 2002.
[14] T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning. Springer Series in Statistics. Springer, 2001.
[15] E. Lehmann and J. Romano. Testing Statistical Hypotheses (3rd ed.). Springer, 2005.
[16] J. Louradour, K. Daoudi, and F. Bach. Feature space mahalanobis sequence kernels: Application to svm speaker verification. IEEE Transactions on Audio, Speech and Language Processing, 2007. To appear.
[17] J. Shawe-Taylor and N. Cristianini. Kernel Methods for Pattern Analysis. Cambridge Univ. Press, 2004.
[18] I. Steinwart, D. Hush, and C. Scovel. An explicit description of the reproducing kernel hilbert spaces of gaussian RBF kernels. IEEE Transactions on Information Theory, 52:4635–4643, 2006.
[19] G. Wahba. Spline Models for Observational Data. SIAM, 1990. 8