L0-regularized high-dimensional sparse multiplicative models

Hao Ming, Hu Yang and Xiaochao Xia

Statistical Theory and Related Fields, 2025, vol. 9, issue 1, 59-83

Abstract: In this paper, we study high-dimensional sparse multiplicative models for positive response data and propose a variable sorted active set (VSAS) algorithm for finding the $ L_0 $ L0 regularized least product relative error (LPRE) estimator. The VSAS algorithm is derived from the local quadratic approximation based on the Karush-Kuhn-Tucker (KKT) conditions of $ L_0 $ L0-penalized LPRE objective function. Under the condition of restricted invertibility, we establish an explicit $ L_\infty $ L∞ upper bound for the sequence of solutions generated by the VSAS algorithm. We further obtain an optimal convergence rate for the proposed estimator with high probability in finite iterations. In addition, our estimator enjoys the oracle property with high probability if the target signal exceeds the detectable level. Finally, extensive simulations and two real-world applications are conducted to illustrate the effectiveness of the proposal.

Date: 2025
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DOI: 10.1080/24754269.2025.2460148

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