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Kernel Sliced Inverse Regression: Regularization and Consistency

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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, Hindawi, vol. 2013, pages 1-11, July.
    • Handle: RePEc:hin:jnlaaa:540725
    DOI: 10.1155/2013/540725
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    Cited by:

    1. Eliana Christou & Annabel Settle & Andreas Artemiou, 2021. "Nonlinear dimension reduction for conditional quantiles," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 937-956, December.
    2. Cho, Youngjoo & Zhan, Xiang & Ghosh, Debashis, 2022. "Nonlinear predictive directions in clinical trials," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).

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