  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 an
empirical study employing deep neural network architecture on three datasets
and convolutional neural network on four datasets. The empirical study showed
better performance for the new regularization approach in five out of the seven
datasets.
