Diffusion Generative Tucker-Unet and Distributional Counterfactual Inference

孔新兵，现为东南大学统计与数据科学学院教授、副院长。主要研究兴趣为高频和高维计量经济学、机器学习、数据科学及其应用；在统计学四大刊AoS、JASA、Biometrika和计量经济学顶刊 JoE、JBES发表论文25篇，其中以独立作者在统计学四大刊发表论文3篇；主持国家自然科学基金项目和课题5项，其中重点专项项目1项；主持中钢集团CAD对象识别和自动算量系统、招商银行南京分行大模型应用、马上消费金融服务有限公司智能体开发等多个企业应用项目。获第一届统计科学技术进步奖一等奖，江苏省教育系统先进个人（优秀教师），完成省教育教学改革重点项目1项，参编统计学101教材《统计机器学习》。担任JBES期刊编委。现为国际统计学会当选会员(ISI elected member)，中国现场统计研究会多元分析应用专业委员会副理事长，江苏省应用统计学会副理事长，江苏概率统计学会理事长。 

Counterfactual analysis with panel and multi-way data often requires recovering an unobserved block of potential outcomes from its factual complement. Existing factor-based completion methods principally produce point predictions or common components, whereas distributional counterfactual analysis requires the conditional law of the missing block. We develop Counterfactual Tucker Diffusion (CFT-Diff), a high dimensional conditional tensor diffusion model via constructing a principled Tucker-Unet architecture. A prespecified mask partitions a low-Tucker-rank tensor into treated counterfactual entries and factual controls; the forward process corrupts only the treated entries and the reverse process conditions on the fixed controls. CFT-Diff fits its score over a structured masked Tucker class: masked Tucker encoders, a low-dimensional core regression, a Tucker decoder, and a skip connection. The resulting reverse diffusion generates repeated counterfactual completions and hence distributional summaries of the missing block. Our theory provides distributional guarantees for treated potential outcomes, and the convergence rates rely on the Tucker core dimension, the maximum mode dimension, and the effective treated dimension, rather than the ambient data dimension. Thus, CFT-Diff provides a statistically parsimonious and computationally efficient approach to distributional counterfactual imputation and inference.