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Kernel Sliced Inverse Regression: Regularization and Consistency

Author

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  • Qiang Wu
  • Feng Liang
  • Sayan Mukherjee

Abstract

Kernel sliced inverse regression (KSIR) is a natural framework for nonlinear dimension reduction using the mapping induced by kernels. However, there are numeric, algorithmic, and conceptual subtleties in making the method robust and consistent. We apply two types of regularization in this framework to address computational stability and generalization performance. We also provide an interpretation of the algorithm and prove consistency. The utility of this approach is illustrated on simulated and real data.

Suggested Citation

  • Qiang Wu & Feng Liang & Sayan Mukherjee, 2013. "Kernel Sliced Inverse Regression: Regularization and Consistency," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:540725
    DOI: 10.1155/2013/540725
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    References listed on IDEAS

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    1. Louis Ferré & Nathalie Villa, 2006. "Multilayer Perceptron with Functional Inputs: an Inverse Regression Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 807-823, December.
    2. He, Guozhong & Müller, Hans-Georg & Wang, Jane-Ling, 2003. "Functional canonical analysis for square integrable stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 54-77, April.
    3. Lexin Li & Xiangrong Yin, 2008. "Sliced Inverse Regression with Regularizations," Biometrics, The International Biometric Society, vol. 64(1), pages 124-131, March.
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    Cited by:

    1. Xu, Jianjun & Zhao, Yue & Cheng, Haoyang, 2025. "Online kernel sliced inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).

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