聚合数据会扭曲用户行为模型，导致误判最佳曝光次数。
Simpson's Paradox in Behavioral Curves: How Aggregation Distorts Parametric Models of User Dynamics
- 用个体与聚合数据对比，发现行为曲线存在辛普森悖论。
- 用户个体峰值在11次曝光，聚合后升至34次，差距达3倍。
- 适合做推荐/广告系统的研究人员，警惕数据聚合陷阱。
行为曲线建模——将参数函数拟合到参与度与曝光量数据上——是推荐系统、广告投放和临床给药中的标准做法。我们发现，数据聚合会引入系统性偏差：行为曲线中的辛普森悖论。在Goodreads（330万用户，9个类别）中，个体用户在约11次曝光时达到参与度峰值，而聚合数据的峰值出现在约34次，相差3倍，这由存活偏差驱动。Amazon Electronics（1800万条评论）显示5.3倍的偏差。MovieLens-25M（D≈1）作为负控组，确认存活偏差而非聚合本身是根本机制。该偏差对类别粒度、参与度定义方式及分类器校准均具鲁棒性。我们提出合成零模型校准法，解决个体分类中32%的假阳性问题。研究结论适用于任何在差异性流失条件下从聚合曲线估计个体行为参数的场景。
原文摘要 · Abstract (English)
Behavioral curve modeling -- fitting parametric functions to engagement-versus-exposure data -- is standard practice in recommendation, advertising, and clinical dosing. We show that aggregation introduces a systematic distortion: Simpson's paradox in behavioral curves. On Goodreads (3.3M users, 9 genres), individual users peak at n* approximately 11 exposures while the aggregate peaks at n* approximately 34 -- a 3x gap driven by survival bias. Amazon Electronics (18M reviews) shows a 5.3x distortion. MovieLens-25M (D approximately 1) serves as a negative control, confirming that survival bias -- not aggregation per se -- is the operative mechanism. The distortion is robust to category granularity, engagement operationalization, and classifier calibration. We develop Synthetic Null Calibration to address a 32% false positive rate in per-user classification. Our findings apply wherever individual behavioral parameters are estimated from aggregate curves under differential attrition.
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