发表机构
Southeast University; University of Science and Technology of China（东南大学; 中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对高维张量设置中的因果推断难题，提出整合处理掩码与塔克结构的条件扩散模型CFTDiff，以高效恢复缺失控制结果的联合条件分布，并在模拟和挪威iFlex实验中验证了其更优的恢复精度与反事实推断能力。
AI 中文摘要
因果推断指导运营和管理决策，但在高维面板或张量设置中仍具挑战性，其中决策可能依赖于缺失控制结果的联合条件分布。我们开发了反事实塔克扩散（Counterfactual Tucker Diffusion, CFTDiff），该方法将处理掩码和潜在塔克结构整合到条件扩散中，通过低维核心中的高效非线性分数学习，在给定观测控制结果的条件下恢复该分布。掩码塔克分数保留了张量模式间的依赖性，同时将非线性分数学习的维度从模式维度的乘积降低到小得多的塔克秩的乘积。我们建立了条件分数估计的高概率误差界，该误差界依赖于塔克秩、最大模式维度以及因子强度调整后的缺失结果数量，并展示了这些界如何转化为缺失控制结果条件分布的恢复保证。在各种缺失率下，模拟显示其点恢复比常见的因果面板和矩阵/张量补全方法更准确；与嵌套扩散规格的比较进一步证明了掩码条件和塔克降维的收益。在挪威的iFlex实验中，CFTDiff比竞争方法更准确地恢复了缺失结果；当应用于因果分析时，其估计的条件分布产生反事实预测区间和目标达成概率，使得定价干预能够通过需求减少幅度和可靠性进行评估。
英文摘要
Causal inference guides operational and managerial decisions but remains challenging in high-dimensional panel or tensor settings, where decisions may depend on the joint conditional distribution of missing control outcomes. We develop \emph{Counterfactual Tucker Diffusion} (\CFTDiff), which integrates the treatment mask and latent Tucker structure into conditional diffusion to recover this distribution given observed control outcomes through efficient nonlinear score learning in a low-dimensional core. The masked Tucker score preserves dependence across tensor modes while reducing the dimension of nonlinear score learning from the product of mode dimensions to the much smaller product of Tucker ranks. We establish high-probability error bounds for conditional score estimation that depend on the Tucker ranks, largest mode dimension, and the factor-strength-adjusted number of missing outcomes, and show how these bounds translate into recovery guaranties for the conditional distribution of the missing control outcomes. Across missing rates, simulations show more accurate point recovery than common causal panel and matrix/tensor completion methods; comparisons with nested diffusion specifications further demonstrate the gains from masked conditioning and Tucker dimension reduction. In Norway's iFlex experiment, \CFTDiff recovers missing outcomes more accurately than competing methods; when applied to causal analysis, its estimated conditional distributions yield counterfactual prediction intervals and target-attainment probabilities, allowing pricing interventions to be evaluated by demand-reduction magnitude and reliability.
