nips nips2007 nips2007-108 nips2007-108-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Kenji Fukumizu, Arthur Gretton, Xiaohai Sun, Bernhard Schölkopf
Abstract: We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments. 1
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17] F. Bach and M. Jordan. Kernel independent component analysis. J. Machine Learning Res., 3:1–48, 2002. C. Baker. Joint measures and cross-covariance operators. Trans. Amer. Math. Soc., 186:273–289, 1973. D. Edwards. Introduction to graphical modelling. Springer verlag, New York, 2000. K. Fukumizu, F. Bach, and A. Gretton. Statistical consistency of kernel canonical correlation analysis. J. Machine Learning Res., 8:361–383, 2007. K. Fukumizu, F. Bach, and M. Jordan. Dimensionality reduction for supervised learning with reproducing kernel Hilbert spaces. J. Machine Learning Res., 5:73–99, 2004. K. Fukumizu, F. Bach, and M. Jordan. Kernel dimension reduction in regression. Tech Report 715, Dept. Statistics, University of California, Berkeley, 2006. ¨ A. Gretton, K. Borgwardt, M. Rasch, B. Scholkopf, and A. Smola. A kernel method for the two-sampleproblem. Advances in NIPS 19. MIT Press, 2007. ¨ A. Gretton, O. Bousquet, A. Smola, and B. Scholkopf. Measuring statistical dependence with HilbertSchmidt norms. 16th Intern. Conf. Algorithmic Learning Theory, pp.63–77. Springer, 2005. ¨ A. Gretton, R. Herbrich, A. Smola, O. Bousquet and B. Sch olkopf. Kernel Methods for Measuring Independence. J. Machine Learning Res., 6:2075–2129, 2005. ¨ A. Gretton, K. Fukumizu, C. Teo, L. Song, B. Scholkopf, A. Smola. A Kernel Statistical Test of Independence. Advances in NIPS 21. 2008, to appear. A. Kraskov, H. St¨gbauer, and P. Grassberger. Estimating mutual information. Physical Review E, 69, o 066138-1–16, 2004. T. Read and N. Cressie. Goodness-of-Fit Statistics for Discrete Multivariate Data. Springer-Verlag, 1988. M. Reed and B. Simon. Functional Analysis. Academic Press, 1980. A. R´ enyi. Probability Theory. Horth-Holland, 1970. I. Steinwart. On the influence of the kernel on the consistency of support vector machines. J. Machine Learning Res., 2:67–93, 2001. ¨ X. Sun, D. Janzing, B. Scholkopf, and K. Fukumizu. A kernel-based causal learning algorithm. Proc. 24th Intern. Conf. Machine Learning, 2007 to appear. S. Fine and K. Scheinberg Efficient SVM Training using Low-Rank Kernel Representations J. Machine Learning Res., 2:243–264, 2001. 8