Do Predictor Envelopes Really Reduce Dimension?

Journal of Data Science

article

Tate Jacobson¹  Hui Zou¹ 

[1] School of Statistics, University of Minnesota

关键词: dimension reduction;    effective degrees of freedom;    envelopes;    Monte Carlo;   

DOI  :  10.6339/21-JDS1017

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

Predictor envelopes model the response variable by using a subspace of dimensiondextracted from the full space of allpinput variables. Predictor envelopes have a close connection to partial least squares and enjoy improved estimation efficiency in theory. As such, predictor envelopes have become increasingly popular in Chemometrics. Often,dis much smaller thanp , which seemingly enhances the interpretability of the envelope model. However, the process of estimating the envelope subspace adds complexity to the final fitted model. To better understand the complexity of predictor envelopes, we study their effective degrees of freedom (EDF) in a variety of settings. We find that in many cases ad -dimensional predictor envelope model can have far more than $d+1$ EDF and often has close to $p+1$. However, the EDF of a predictor envelope depend heavily on the structure of the underlying data-generating model and there are settings under which predictor envelopes can have substantially reduced model complexity.

【 授权许可】

CC BY