A Discrete Measure for Debiased Feature Grouping: A Limit of Moreau-Enhanced OSCAR Regularizer and Its Proximity Operator

Octagonal shrinkage and clustering algorithm for regression (OSCAR) is an effective method for feature grouping, which aims to select important highly-correlated groups of features relevant to the observations. Unfortunately, it is known that OSCAR may cause estimation bias, which is undesirable for many applications. Whereas the Moreau enhancement of convex regularizers promoting sparsity or low-rankness has been studied extensively to reduce the estimation bias, its use in the feature grouping task still remains unexplored. In this paper, we investigate the debiasing effect of the discrete measure defined by a limit of the Moreau-enhanced OSCAR regularizer, which is referred to as the LME-OSCAR regularizer. The proximity operator of the LME-OSCAR regularizer can be computed efficiently by using the dynamic programming. Numerical examples demonstrate the efficacy of the proposed discrete measure.