标题： 因果协变量应该有多平衡？ 显示英文标题

标题： How Balanced Should Causal Covariates Be?

摘要： 协变量平衡是一种在观察性研究中控制混杂因素的流行技术。它为治疗组找到接近均匀的权重，但使该组的协变量均值（近似）等于整个样本的协变量均值。一个关键问题是：为了最小化最终估计值的误差，平衡应该有多接近？目前的指导方针来源于启发式或渐进分析，当样本量相对于协变量数量较小时，这些分析是没有信息量的。本文首次对协变量平衡进行了严格的非渐进分析；具体来说，我们使用PAC-Bayesian技术推导出了治疗效果的有效有限样本置信区间。更一般地，我们证明了这些保证适用于灵活的协变量平衡形式，在这种形式下，平衡偏差（不平衡）和方差（偏离均匀性）之间的权衡正则化参数被优化而不是固定。这催生了一种新的平衡算法，实证结果显示其具有优越的适应性。我们的总体贡献是使协变量平衡成为因果推理的一种更可靠的方法。 显示英文摘要

摘要： Covariate balancing is a popular technique for controlling confounding in observational studies. It finds weights for the treatment group which are close to uniform, but make the group's covariate means (approximately) equal to those of the entire sample. A crucial question is: how approximate should the balancing be, in order to minimize the error of the final estimate? Current guidance is derived from heuristic or asymptotic analyses, which are uninformative when the size of the sample is small compared to the number of covariates. This paper presents the first rigorous, nonasymptotic analysis of covariate balancing; specifically, we use PAC-Bayesian techniques to derive valid, finite-sample confidence intervals for the treatment effect. More generally, we prove these guarantees for a flexible form of covariate balancing where the regularization parameters weighting the tradeoff between bias (imbalance) and variance (divergence from uniform) are optimized, not fixed. This gives rise to a new balancing algorithm which empirically delivers superior adaptivity. Our overall contribution is to make covariate balancing a more reliable method for causal inference.