Envelope Inverse Regression for Dimension Reduction: A Review and New Perspectives

ZENG Jing, WANG Ning, ZHANG Xin

Journal of Systems Science & Complexity ›› 2025

PDF(473 KB)
PDF(473 KB)
Journal of Systems Science & Complexity ›› 2025

Envelope Inverse Regression for Dimension Reduction: A Review and New Perspectives

  • ZENG Jing1, WANG Ning1, ZHANG Xin2
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Abstract

In this note, we revisit the envelope dimension reduction, which was first introduced for estimating a sufficient dimension reduction subspace without inverting the sample covariance. Motivated by the recent developments in envelope methods and algorithms, we refresh the envelope inverse regression as a flexible alternative to the existing inverse regression methods in dimension reduction. We discuss the versatility of the envelope approach and demonstrate the advantages of the envelope dimension reduction through simulation studies.

Key words

Envelope model / subspace estimation / sufficient dimension reduction

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ZENG Jing , WANG Ning , ZHANG Xin. Envelope Inverse Regression for Dimension Reduction: A Review and New Perspectives. Journal of Systems Science & Complexity, 2025

Funding

Zeng’s research was supported by National Natural Science Foundation of China (NNSFC) under Grant No. 12301365. Wang’s research was supported by NNSFC under Grant No. 2241200071.
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