A new type of generalized information criterion for regularization parameter selection in penalized regression with application to treatment process data

ABSTRACT

We propose a new approach to select the regularization parameter using a new version of the generalized information criterion ($\mathit{GIC}$) in the subject of penalized regression. We prove the identifiability of bridge regression model as a prerequisite of statistical modeling. Then, we propose asymptotically efficient generalized information criterion ($\mathit{AGIC}$) and prove that it has asymptotic loss efficiency. Also, we verified the better performance of $\mathit{AGIC}$ in comparison to the older versions of $\mathit{GIC}$. Furthermore, we propose $\mathit{MSE}$ search paths to order the selected features by lasso regression based on numerical studies. The $\mathit{MSE}$ search paths provide a way to cover the lack of feature ordering in lasso regression model. The performance of $\mathit{AGIC}$ with other types of $\mathit{GIC}$ is compared using $\mathit{MSE}$ and model utility in simulation study. We exert $\mathit{AGIC}$ and other criteria to analyze breast and prostate cancer and Parkinson disease datasets. The results confirm the superiority of $\mathit{AGIC}$ in almost all situations.

KEYWORDS:

• Asymptotic Loss Efficiency
• generalized information criterion
• penalized regression
• regularization parameter
• utility function

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The codes are available upon request.

2. $\mathit{https}://\mathit{data}.\mathit{world}/\mathit{exercises}/\mathit{linear}-\mathit{regression}-\mathit{exercise}-1/\mathit{workspace}/\mathit{data}-\mathit{dictionary}$

3. https://archive.ics.uci.edu/ml/datasets/Parkinsons+Telemonitoring

Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.