A novel nonconvex, smooth-at-origin penalty for statistical learning

Majnu John (), Sujit Vettam () and Yihren Wu ()
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Majnu John: Hofstra University
Sujit Vettam: University of Chicago
Yihren Wu: Hofstra University

Computational Statistics, 2025, vol. 40, issue 3, No 10, 1397-1422

Abstract: Abstract Nonconvex penalties are utilized for regularization in high-dimensional statistical learning algorithms primarily because they yield unbiased or nearly unbiased estimators for the parameters in the model. Nonconvex penalties existing in the literature such as SCAD, MCP, Laplace and arctan have a singularity at origin which makes them useful also for variable selection. However, in several high-dimensional frameworks such as deep learning, variable selection is less of a concern. In this paper, we present a nonconvex penalty which is smooth at origin. The paper includes asymptotic results for ordinary least squares estimators regularized with the new penalty function, showing asymptotic bias that vanishes exponentially fast. We also conducted simulations to better understand the finite sample properties and conducted an empirical study employing deep neural network architecture on three datasets and convolutional neural network on four datasets. The empirical study based on artificial neural networks showed better performance for the new regularization approach in five out of the seven datasets.

Keywords: Regularization; Nonconvex penalties; High-dimensional statistics; Deep learning; Artificial neural network; Convolutional neural network (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01525-x

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