arXiv Machine Learning September 3, 2026 By Haruka Tanzawa, Ayaka Sakata

Stabilizing Private LASSO under Heterogeneous Covariates via Anisotropic Objective Perturbation

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The paper investigates high‑dimensional LASSO under differential privacy using objective perturbation when covariates have heterogeneous scales. It introduces a Gram‑based anisotropic objective perturbation that counteracts the distortion caused by covariate heterogeneity, restoring isotropy in the estimation process. Through an Approximate Message Passing framework and state evolution analysis, the authors show that this approach stabilizes convergence and improves both statistical efficiency and privacy performance compared to standard uniform noise injection.

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