AI 中文总结
针对网络干扰下的离策略因果估计难题，本文基于傅里叶基构建最小L²权重，推导鲁棒性界、一致性条件与方差估计量，通过仿真验证其在实验设计分析中的有效性。
AI 中文摘要
在存在干扰（即分配给一个单元的处理会影响其他单元的结果）的情况下，许多因果估计量取决于开展实验所依据的处理分配策略。这种策略依赖性为离策略估计带来了根本性挑战，离策略估计的目标是估计与收集数据所用策略不同的假设干预策略下的因果量。我们针对异质伯努利策略下的因果效应离策略估计问题展开研究。通过将暴露加权潜在结果表示为实验设计的有偏傅里叶基，我们针对任何预先指定的编码假设干扰结构的傅里叶子空间，构建了唯一的最小L²权重，该权重可迁移该子空间中的每个函数。全局和局部逆概率权重、线性干扰权重以及无干扰权重均为其特例。权重方差是实验策略与目标策略之间的结构化卡方距离。当假设的干扰结构设定错误时，引入的偏差会将被遗漏的结果谱与相应的策略转移系数耦合，从而得到一个精确的鲁棒性界和一个偏差-方差权衡。傅里叶邻域重叠条件保证了结构化干扰下的一致性，我们为离策略估计量提出了杜布鞅中心极限定理。由于方差无法识别，我们推导了可识别的界及相关的保守方差估计量。仿真结果阐明了这些理论结果在网络干扰和设定不匹配情况下的实验设计与分析中的应用。
英文摘要
In the presence of interference, where the treatment assigned to one unit can affect the outcomes of others, many causal estimands depend on the treatment-assignment policy under which the experiment is conducted. This policy dependence creates a fundamental challenge for off-policy estimation, where the goal is to estimate causal quantities under a hypothetical intervention policy different from the one used to collect data. We study this problem of off-policy estimation of causal effects for heterogeneous Bernoulli policies. By representing exposure-weighted potential outcomes in the biased Fourier basis of the experimental design, we construct, for any prespecified Fourier subspace encoding the assumed interference structure, the unique minimum-$L^2$ weight that transports every function in that subspace. Global and local inverse-probability weights, linear-interference weights, and no-interference weights are special cases. The weight variance is a structured chi-square distance between the experiment and target policies. When the assumed interference structure is misspecified, the introduced bias couples the omitted outcome spectrum with the corresponding policy-shift coefficients, yielding a sharp robustness bound and a bias-variance trade-off. A Fourier-neighborhood-overlap condition gives consistency under structured interference, and we state a Doob-martingale central limit theorem for off-policy estimators. As the variance is not identified, we derive identifiable bounds and associated conservative estimators of the variance. Simulations illustrate these theoretical results for the design and analysis of experiments under network interference and design mismatch.
Comments17 pages, 1 figure
