Principal Covariate Regression with Nuclear Norm Penalty

2026-06-22

AI Summary

This work proposes a novel method—nuclear-norm-penalized principal covariates regression (PcovR-nnp)—to address the challenges of high-dimensional regression, where dimensionality reduction and regularized coefficient estimation are typically performed sequentially in an ad hoc order, compromising model stability. By introducing the nuclear norm into the principal covariates regression framework for the first time, PcovR-nnp jointly optimizes matrix decomposition and regularized regression, thereby simultaneously achieving dimension selection and coefficient estimation. This integrated approach eliminates the need for subjective, stepwise procedural choices inherent in conventional pipelines and substantially enhances both the accuracy and robustness of high-dimensional regression modeling.

Abstract

In high-dimensional data settings, dimensionality reduction or variable selection are key steps when using statistical learning techniques. Principal Covariate Regression-type methods aim to perform both dimensionality reduction and (regularized) regression steps in one analysis. However, existing PCovR methods cannot simultaneously select dimensionalities and estimate regularized coefficients, forcing researchers to make ad-hoc choices in the order of these steps. In this study, we propose a novel method called Principal Covariate Regression with Nuclear Norm Penalty (PcovRnnp) that allows simultaneous dimension reduction and estimation of regularized coefficients.

Problem

• Principal Covariate Regression
• dimensionality reduction
• regularized regression
• high-dimensional data
• nuclear norm penalty

Innovation

• Principal Covariate Regression
• Nuclear Norm Penalty
• Dimensionality Reduction
• Regularized Regression
• High-dimensional Data