# A unified consensus-based parallel ADMM algorithm for high-dimensional regression with combined regularizations Source: [A unified consensus-based parallel ADMM algorithm for high-dimensional regression with combined regularizations]() Collection index: [llms.txt]() Data updated: 2025-10-27T05:29:32.828Z Authors: Xiaofei Wu, Zhimin Zhang, Zhenyu Cui Published: 2023-11-21T03:30:38.000Z ## Abstract The parallel alternating direction method of multipliers (ADMM) algorithm is widely recognized for its effectiveness in handling large-scale datasets stored in a distributed manner, making it a popular choice for solving statistical learning models. However, there is currently limited research on parallel algorithms specifically designed for high-dimensional regression with combined (composite) regularization terms. These terms, such as elastic-net, sparse group lasso, sparse fused lasso, and their nonconvex variants, have gained significant attention in various fields due to their ability to incorporate prior information and promote sparsity within specific groups or fused variables. The scarcity of parallel algorithms for combined regularizations can be attributed to the inherent nonsmoothness and complexity of these terms, as well as the absence of closed-form solutions for certain proximal operators associated with them. In this paper, we propose a unified constrained optimization formulation based on the consensus problem for these types of convex and nonconvex regression problems and derive the corresponding parallel ADMM algorithms. Furthermore, we prove that the proposed algorithm not only has global convergence but also exhibits linear convergence rate. Extensive simulation experiments, along with a financial example, serve to demonstrate the reliability, stability, and scalability of our algorithm. The R package for implementing the proposed algorithms can be obtained at https://github.com/xfwu1016/CPADMM. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Music Genre Classification on FMA small (test)](): Music Genre Classification; FMA small (test); Accuracy: 92.96. - [Music Genre Classification on FMA small (train)](): Music Genre Classification; FMA small (train); Sparsity: 85.99. ## Original sources and implementation [Original paper]() [PDF]()