Journal Article

Tensor Envelope Partial Least-Squares Regression

Zhang, Xin, Li, Lexin

2017

Overview

Partial least squares (PLS) is a prominent solution for dimension reduction and high-dimensional regressions. Recent prevalence of multidimensional tensor data has led to several tensor versions of the PLS algorithms. However, none offers a population model and interpretation, and statistical properties of the associated parameters remain intractable. In this article, we first propose a new tensor partial least-squares algorithm, then establish the corresponding population interpretation. This population investigation allows us to gain new insight on how the PLS achieves effective dimension reduction, to build connection with the notion of sufficient dimension reduction, and to obtain the asymptotic consistency of the PLS estimator. We compare our method, both analytically and numerically, with some alternative solutions. We also illustrate the efficacy of the new method on simulations and two neuroimaging data analyses. Supplementary materials for this article are available online.

• Publisher: Taylor & Francis,American Society for Quality and the American Statistical Association,American Society for Quality
• Subject: Algorithms / Asymptotic methods / Computer simulation / Data analysis / Dimension reduction / Least squares method / Mathematical models / Medical imaging / Multidimensional array / Neuroimaging analysis / Neurology / Partial least squares / Population (statistical) / Reduced rank regression / Reduction / Regression analysis / Sparsity principle / Statistical analysis / Tensors