Constrained Dantzig-type estimator with k-support norm

Abstract

We propose a novel extension of the Constrained Dantzig Estimator (CDE) by substituting the conventional l1 norm regularization with the k-support norm, a convex penalty that better balances sparsity and feature correlation. While the original CDE provided a principled approach to sparse regression under linear equality constraints, its reliance on the l1 criterion may ignore relevant correlated features. The k-support norm addresses this limitation by interpolating between the l1 and l2 norm, facilitating sparsity and offering greater flexibility in high-dimensional settings. We present preliminary theoretical results toward establishing an error bound for our proposed model. Moreover, performance evaluation is conducted on both synthetic and real-world datasets, demonstrating the sparsity and accuracy advantages of the proposed method through comprehensive comparisons against existing estimators.