切片 $L^p$ 分布平衡
Sliced $L^p$ Distributional Balancing
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中文总结 AI 辅助
本文提出切片 $L^p$ 分布平衡（SLDB）方法，通过一维投影的 $L^p$ 距离加权平衡协变量分布，并开发高效算法及理论框架，实现因果效应的有效估计。
中文摘要 AI 辅助
一类流行的因果推断方法通过加权处理混杂问题，即在不使用结局信息的情况下对处理组和对照组进行重新加权以平衡其协变量分布，从而保持基于设计的视角。在本文中，我们提出了切片 $L^p$ 分布平衡（SLDB），这是一个由 $p\in[1,\infty)$ 索引的族，通过平均一维线性投影的累积分布函数之间的平方 $L^p$ 距离来衡量不平衡。Cramér--Wold 装置确保该准则能识别多元分布的相等性，而投影将其计算简化为基于排序的一维操作。由于我们的方法位于许多现有分布平衡方法所依赖的最大均值差异（MMD）框架之外，其理论和计算工具不能直接适用。因此，我们开发了一种计算高效的投影次梯度下降算法来估计平衡权重，与基于 MMD 的方法相比，提供了改进的计算复杂度。此外，我们建立了基于 SLDB 的因果效应估计的新理论框架，并在适当条件下证明了 $\sqrt{n}$ 一致性和渐近正态性，其渐近方差达到半参数效率界。最后，我们开发了不需要结局模型增强的推断程序，从而保留了基于设计的原则。模拟研究和实际应用表明，SLDB 与现有方法相比具有竞争力。
英文摘要
A popular class of causal inference methods addresses confounding through weighting, which reweights treated and control groups to balance their covariate distributions without using outcome information, thereby preserving a design-based perspective. In this paper, we propose sliced $L^p$ distributional balancing (SLDB), a family indexed by $p\in[1,\infty)$ that measures imbalance by averaging squared $L^p$ distances between the cumulative distribution functions of one-dimensional linear projections. The Cramér--Wold device ensures that this criterion identifies equality of multivariate distributions, while projection reduces its computation to sorting-based one-dimensional operations. Because our method lies outside the maximum mean discrepancy (MMD) framework underlying many existing distributional balancing methods, their theoretical and computational tools do not directly apply. We therefore develop a computationally efficient projected subgradient descent algorithm for estimating balancing weights, offering improved computational complexity over MMD-based methods. Furthermore, we establish a novel theoretical framework for SLDB-based causal effect estimation and prove, under suitable conditions, root-n consistency and asymptotic normality, with the asymptotic variance attaining the semiparametric efficiency bound. Finally, we develop inferential procedures that do not require augmentation with an outcome model, thereby retaining the design-based principle. Simulation studies and a real-world application demonstrate that SLDB performs competitively with existing methods.
发表机构
- University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
- University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
机构由 AI 辅助整理，请以论文原文为准。
