Multiple penalized regularization for clusters with varying correlation levels

In this paper, we study the high-dimensional correlated data with multi-level correlations. These data appear frequently in many fields, e.g., genes in gene pathways or stock in industry groups. It motivates us not only to exploit these clusters but also to distinguish the correlation levels. Besides, we analyze the data without pre-specified clustering information to covariates. A two-step method is proposed to address the above problems. The first step focuses on distinguishing the levels and clustering. We aim to divide covariates into sub-vectors, considering both grouping effect and varying correlation. In the second step, we propose a joint estimation and a modified coordinate descent algorithm. The proposed procedure estimates different correlated groups with different penalties. We provide the theoretical guarantees of this method. Numerical comparisons show that the method works effectively on the multi-level correlation structures. We also apply the proposed method to financial data and get interpretable results.

Keywords

multi-level correlations, clustering, elastic net, structured sparsity

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This work was supported by the National Natural Science Foundation of China (Grant No. 12001557), the Youth Talent Development Support Program (QYP202104), the Emerging Interdisciplinary Project, the Program for Innovation Research, the Disciplinary Funding, and the School of Statistics and Mathematics in Central University of Finance and Economics.

W. Cao and L. Wang contributed equally to this work.

Received 1 June 2021

Accepted 21 August 2021

Published 14 February 2022