DROP：在图形模型中的多任务学习中的分布鲁棒优化
DROP: Distributionally Robust Optimization for Multi-task Learning in Graphical Models
AI总结：
本文提出DROP方法，通过多任务节点回归框架实现鲁棒估计，理论证明其在数据污染下的误差界，并通过模拟和fMRI应用展示其在高维数据中的优越性。
摘要：
高斯图形模型（GGMs）广泛用于推断高维数据中的条件依赖结构。然而，标准精度矩阵估计器对数据污染（如极端异常值和重尾噪声）非常敏感。本文提出DROP（分布鲁棒优化），一种在多任务节点回归框架内提出的鲁棒估计方法。所提估计器在保持结构稀疏性的同时，能抵抗受污染观测的影响。理论上，在一般污染下建立了DROP估计器的误差界。通过广泛的高维模拟，证明DROP能一致控制假阳性边的速率，并在数据偏离标准高斯假设时优于传统非鲁棒估计器。此外，在功能性磁共振成像（fMRI）应用中，DROP在严重数据扰动下仍能保持稳定的图结构并保留网络模块性，而竞争方法则产生过于密集的网络。为促进可重复研究，DROP R包将在GitHub上公开发布。
英文摘要：
Gaussian Graphical Models (GGMs) are widely used to infer conditional dependence structures in high-dimensional data. However, standard precision matrix estimators are highly sensitive to data contamination, such as extreme outliers and heavy-tailed noise. In this paper, we propose DROP (Distributionally Robust Optimization), a robust estimation method formulated within a multi-task nodewise regression framework. The proposed estimator enforces structural sparsity while resisting the influence of corrupted observations. Theoretically, we establish error bounds for the DROP estimator under general contamination. Through extensive high-dimensional simulations, we demonstrate that DROP consistently controls the rate of false positive edges and outperforms conventional non-robust estimators when data deviate from standard Gaussian assumptions. Furthermore, in a functional MRI (fMRI) application, DROP maintains a stable graph structure and preserves network modularity even when subjected to severe data perturbations, whereas competing methods yield excessively dense networks. To facilitate reproducible research, the DROP R package will be made publicly available on GitHub.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
