Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A selective review of nonlinear sufficient dimension reduction

  • Sehun Jang (Department of Statistics, Korea University) ;
  • Jun Song (Department of Statistics, Korea University)
  • Received : 2024.01.21
  • Accepted : 2024.01.30
  • Published : 2024.03.31
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Abstract

In this paper, we explore nonlinear sufficient dimension reduction (SDR) methods, with a primary focus on establishing a foundational framework that integrates various nonlinear SDR methods. We illustrate the generalized sliced inverse regression (GSIR) and the generalized sliced average variance estimation (GSAVE) which are fitted by the framework. Further, we delve into nonlinear extensions of inverse moments through the kernel trick, specifically examining the kernel sliced inverse regression (KSIR) and kernel canonical correlation analysis (KCCA), and explore their relationships within the established framework. We also briefly explain the nonlinear SDR for functional data. In addition, we present practical aspects such as algorithmic implementations. This paper concludes with remarks on the dimensionality problem of the target function class.

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Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1C1C1003647, No. RS-2023-00219212, and No. 2022M3J6A1063595) and a Korea University Grant (K2312771).

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