Interpretable Scalar-on-Image Linear Regression Models via the Generalized Dantzig Selector

• 成果类型: Article; Early Access
• 署名作者: Liao, Sijia; Sun, Xiaoxiao; Hao, Ning; Zhang, Hao Helen
• 署名单位: University of Arizona; University of Arizona; University of Arizona
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2690121
• 发表日期: 2026-07-23
• 关键词: Bivariate function; Non-asymptotic error bound; Nonparametric Regression; Smoothness regularization; Sparse Estimation; variable selection; splines; parameter; sparsity

摘要

The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness constraints to control the bias-variance trade-off, and thus prevent overfitting. However, such assumptions can hinder interpretability, especially when only certain regions of an image influence changes in the response. In such a scenario, interpretability can be better captured by imposing sparsity assumptions on the coefficient function. To address this challenge, we propose the Generalized Dantzig Selector, a novel method that jointly enforces sparsity and smoothness on the coefficient function. The proposed approach enhances interpretability by accurately identifying regions with no contribution to the changes of response, while preserving stability in estimation. Extensive simulation studies and real data applications demonstrate that the new method is highly interpretable and achieves notable improvements over existing approaches. Moreover, we rigorously establish non-asymptotic bounds for the estimation error, providing strong theoretical guarantees for the proposed framework. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.