On two recent nonconvex penalties for regularization in machine learning

Regularization methods are often employed to reduce overfitting of machine learning models. Nonconvex penalty functions are often considered for regularization because of their near-unbiasedness properties. In this paper, we consider two relatively new penalty functions: Laplace and arctan, and show how they fit into certain recently introduced statistical and optimization frameworks. We also compare empirically the performance of the two new penalty functions with existing penalty functions utilized as regularizers of deep neural networks and convolutional neural networks on seven different datasets.