Sufficient dimension folding via tensor inverse regression

ABSTRACT

Sufficient dimension reduction (SDR) techniques have proven to be very useful data analysis tools in various applications. Conventional SDR methods mainly tackle simple vector-valued predictors, but they are inappropriate for data with array (tensor)-valued predictors. In this paper, we propose a tensor dimension reduction approach based on inverse regression, and we refer to it as T-IRE, which reduces the dimension of original array-valued predictors while simultaneously retaining the structural information within predictors and the proposed method also provides an efficient estimation algorithm. Empirical performance and two dataset analysis demonstrate the advantages of our proposed method.

KEYWORDS:

• Inverse regression estimation
• tensor-valued data
• sufficient dimension folding

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62H12
• 53A45
• 62H99

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Xiangjie Li  http://orcid.org/0000-0002-9600-8984

Additional information

Funding

This work was supported by the Project funded by China Postdoctoral Science Foundation and by the MOE Project of key Research Institute of Humanities and Social Sciences at Universities [grant number 16JJD910002].