Tuning parameter selection for the adaptive nuclear norm regularized trace regression

TL;DR

This paper proposes a Bayesian information criterion (BIC) for selecting tuning parameters in adaptive nuclear norm regularized trace regression, ensuring rank consistency and improving model performance in high-dimensional data analysis.

Contribution

The paper introduces a BIC based on an unbiased degrees of freedom estimator for adaptive nuclear norm regularized trace regression, with proven rank consistency.

Findings

BIC achieves rank consistency under regularized conditions.

Numerical results demonstrate effective tuning parameter selection.

Model solutions converge to true solutions with correct rank.

Abstract

Regularized models have been applied in lots of areas, with high-dimensional data sets being popular. Because tuning parameter decides the theoretical performance and computational efficiency of the regularized models, tuning parameter selection is a basic and important issue. We consider the tuning parameter selection for adaptive nuclear norm regularized trace regression, which achieves by the Bayesian information criterion (BIC). The proposed BIC is established with the help of an unbiased estimator of degrees of freedom. Under some regularized conditions, this BIC is proved to achieve the rank consistency of the tuning parameter selection. That is the model solution under selected tuning parameter converges to the true solution and has the same rank with that of the true solution in probability. Some numerical results are presented to evaluate the performance of the proposed BIC on tuning parameter selection.