发表机构
Academy of Life and Natural Sciences, Xi’an Jiaotong-Liverpool University; Aerospace Information Research Institute, Chinese Academy of Sciences（西交利物浦大学生命与自然科学学院; 中国科学院空天信息研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对不规则历史的纵向因果推断，提出DR-FRL交叉拟合工作流，通过函数与时间编码器映射状态、估计干扰项函数，经诊断验证后在模拟与VitalDB审计中表现出良好性能。
AI 中文摘要
纵向因果研究常将历史记录为不规则的函数片段：实验室值、生理信号、传感器流以及在不等且具有信息性的时间点测量的图像衍生摘要。标准双重鲁棒估计器通常需要标量摘要，而序列学习器优化的预测损失不一定能稳定有效影响函数（EIF）。我们提出双重鲁棒函数表示学习（DR-FRL），这是一种交叉拟合工作流，可将不规则历史转化为针对观测历史 regime 的估计目标状态。函数编码器和时间编码器将点云及先验历史映射为状态；干扰项头估计结局、处理和删失函数；以EIF为目标的验证、校准、重叠、尾部及 ablation 诊断用于评估该状态是否支持估计方程。若所选状态保留了EIF所需的干扰项信息，则表示误差会与普通干扰项误差进入同一二阶乘积余项，且均值估计量在明确的速率、重叠、校准及稳定性条件下渐近线性。Catoni聚合被单独视为有界影响点估计量，而非Wald推断的替代。模拟结果显示，当函数混杂为高维、测量具有信息性、支持薄弱或伪结局为重尾时，DR-FRL表现更优。VitalDB审计表明，DR-FRL可利用不规则实验室点云并得出有用的阴性发现：对于该ICU处置结局，标量实验室摘要已携带大量与结局相关的信息。
英文摘要
Longitudinal causal studies often record histories as irregular functional fragments: laboratory values, physiologic signals, sensor streams, and image-derived summaries measured at unequal and informative times. Standard doubly robust estimators usually require scalar summaries, whereas sequence learners optimize prediction losses that need not stabilize the efficient influence function. We propose Doubly Robust Functional Representation Learning (DR-FRL), a cross-fitted workflow that turns irregular histories into estimand-targeted states for observed-history regimes. Functional and temporal encoders map point clouds and prior histories into states; nuisance heads estimate outcome, treatment, and censoring functions; and EIF-targeted validation, calibration, overlap, tail, and ablation diagnostics assess whether the state supports the estimating equation. If the selected state preserves the nuisance information needed by the EIF, representation error enters the same second-order product remainder as ordinary nuisance error, and the mean estimator is asymptotically linear under explicit rate, overlap, calibration, and stability conditions. Catoni aggregation is treated separately as a bounded-influence point estimator, not a replacement for Wald inference. Simulations show gains when functional confounding is high-dimensional, measurement is informative, support is weak, or pseudo-outcomes are heavy-tailed. A VitalDB audit shows that DR-FRL can use irregular laboratory point clouds and deliver a useful negative finding: for this ICU-disposition endpoint, scalar laboratory summaries already carry much endpoint-relevant information.
