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Kernel dimension reduction in regression (2006)

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by Kenji Fukumizu , Francis R. Bach , Michael I. Jordan
Citations:19 - 11 self
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BibTeX

@TECHREPORT{Fukumizu06kerneldimension,
    author = {Kenji Fukumizu and Francis R. Bach and Michael I. Jordan},
    title = {Kernel dimension reduction in regression},
    institution = {},
    year = {2006}
}

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Abstract

Acknowledgements. The authors thank the editor and anonymous refer-ees for their helpful comments. The authors also thank Dr. Yoichi Nishiyama for his helpful comments on the uniform convergence of empirical processes. We would like to acknowledge support from JSPS KAKENHI 15700241,

Citations

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104 On the influence of the kernel on the consistency of support vector machines - Steinwart - 2001
101 der Vaart. Asymptotic Statistics - van - 2000
79 Dimensionality reduction for supervised learning with reproducing kernel hilbert spaces - Fukumizu, Bach, et al. - 2004
61 Measuring statistical dependence with Hilbert-Schmidt norms - Gretton, Bousquet, et al. - 2005
59 Functional Analysis - Lax - 2003
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49 On principal Hessian directions for data visualization and dimension reduction: Another application of Stein’s lemma - Li - 1992
33 Joint measures and cross-covariance operators - Baker - 1973
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28 Multivariate Statistics: A Practical Approach - Flury, Riedwyl - 1988
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16 Dimension reduction for the conditional mean in regression - Cook, Li - 2002
16 An adaptive estimation of dimension reduction - Xia, Tong, et al.
13 Structure adaptive approach for dimension reduction - Hristache, Juditsky, et al. - 2001
12 Statistical consistency of kernel canonical correlation analysis - Fukumizu, Bach, et al. - 2007
10 Contour regression: A general approach to dimension reduction - Li, Zha, et al. - 2005
10 Discussion of Li - Cook, Weisberg - 1991
8 Dimension reduction in regression with a binary response - Cook, Lee - 1999
7 Consistency of kernel canonical correlation analysis - Fukumizu, Bach, et al. - 2005
6 An Adaptive Estimation of Dimension Reduction Space - Xia, Tong, et al. - 2002
5 Sufficient dimension reduction and graphics in regression - Chiaromonte, Cook - 2002
3 Direction estimation in single-index regressions - Yin, Cook - 2005
2 Moment-based dimension reduction for multivariate response regression - Yin, Bura - 2006
2 Fourier methods for estimating the central subspace and the central mean subspace in regression - Zhu, Zeng - 2006
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