发表机构
Uppsala University; Science for Life Laboratory（乌普萨拉大学; 生命科学实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Wasserstein DRO线性回归，统一平方根Lasso与对抗线性回归，证明其误差界、枢轴性质及解等价性，并验证高效求解。
AI 中文摘要
分布鲁棒优化（DRO）研究在基础概率分布不确定性下的参数估计，并已成为分析鲁棒性和泛化性的原则性框架。特别是，由Wasserstein距离引起的分布不确定性的Wasserstein DRO，推广了几种流行的正则化器。本文研究Wasserstein DRO线性回归，将平方根Lasso和对抗线性回归作为重要的特例统一起来。我们证明了这两个特例的许多性质可以推广到这一通用方法。具体而言，我们展示了（i）确定性且非渐近的样本内误差界，一般情况下为$O(n^{-1/2})$，在设计矩阵和稀疏性条件下为$O(n^{-1})$；（ii）对噪声水平的不敏感性，也称为枢轴性质；（iii）小和大模糊集下的解等价性。关键的证明步骤是将该方法重新表述为二次形式，模仿对抗线性回归。我们还表明该方法可以高效求解，并通过数值模拟验证了我们的发现。
英文摘要
Distributionally robust optimization (DRO) studies parameter estimation under uncertainty in the underlying probability distribution and has emerged as a principled framework for analyzing robustness and generalization. In particular, Wasserstein DRO, with distributional uncertainty induced by the Wasserstein distance, generalizes several popular regularizers. This paper studies Wasserstein DRO linear regression, unifying square-root Lasso and adversarial linear regression as important special cases. We prove that many properties of these two special cases carry over to this general method. In particular, we show (i) deterministic and non-asymptotic in-sample error bounds $O(n^{-1/2})$ in general and $O(n^{-1})$ under design matrix and sparsity conditions; (ii) insensitivity to the noise level, also known as the pivotal property; and (iii) solution equivalences for small and large ambiguity sets. The key proof step is to recast the method into a quadratic form, mimicking adversarial linear regression. We also show that the method can be solved efficiently, and we validate our findings through numerical simulations.
