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Kernel dimension reduction in regression
Open accessAbstract
We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate X from the response Y, given the projection of X on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316–342 and Regression Graphics (1998) Wiley]. We show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel Hilbert spaces and we show how this characterization leads to an M-estimator for the central subspace. The resulting estimator is shown to be consistent under weak conditions; in particular, we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for SDR methods. We also present empirical results showing that the new methodology is competitive in practice.
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Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
Spline Models for Observational Data
Wahba, G. (1990) · doi:10.1137/1.9781611970128 · Cited by 4,184
Cited by
Data-Driven Intelligent Transportation Systems: A Survey
Zhang, J., Wang, F.-Y., Wang, K., Lin, W.-H., Xu, X., & Chen, C. (2011) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2011.2158001 · Cited by 1,817
Kernel Mean Embedding of Distributions: A Review and Beyond
Muandet, K., Fukumizu, K., Sriperumbudur, B., & Schölkopf, B. (2017) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000060 · Cited by 409
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Metadata
- Authors
- Fukumizu, K., Bach, F. R., & Jordan, M. I.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 2009-08-01
- Volume
- 37
- Issue
- 4
- Pages
- 1871-1905
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2072460512
- Cited by
- 289
- References
- 2
- FWCI
- 17.22
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Fukumizu, K., Bach, F. R., & Jordan, M. I. (2009). Kernel dimension reduction in regression. The Annals of Statistics. https://doi.org/10.1214/08-aos637
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