We consider sequential treatment regimes where each unit is exposed to combinations of interventions over time. When interventions are described by qualitative labels, such as "close schools for a month due to a pandemic" or "promote this podcast to this user during this week", it is unclear which appropriate structural assumptions allow us to generalize behavioral predictions to previously unseen combinations of interventions. Standard black-box approaches mapping sequences of categorical variables to outputs are applicable, but they rely on poorly understood assumptions on how reliable generalization can be obtained, and may underperform under sparse sequences, temporal variability, and large action spaces. To approach that, we pose an explicit model for composition, that is, how the effect of sequential interventions can be isolated into modules, clarifying which data conditions allow for the identification of their combined effect at different units and time steps. We show the identification properties of our compositional model, inspired by advances in causal matrix factorization methods. Our focus is on predictive models for novel compositions of interventions instead of matrix completion tasks and causal effect estimation. We compare our approach to flexible but generic black-box models to illustrate how structure aids prediction in sparse data conditions.

翻译：我们考虑序列治疗策略，其中每个单元随时间暴露于干预的组合。当干预由定性标签描述时，例如"因疫情关闭学校一个月"或"在本周向该用户推广此播客"，目前尚不清楚哪种适当的结构假设允许我们将行为预测推广到先前未见过的干预组合。将分类变量序列映射到输出的标准黑盒方法虽然适用，但它们依赖于对如何获得可靠推广的、理解不足的假设，并且在稀疏序列、时间变异性和较大动作空间下可能表现不佳。为此，我们提出了一个明确的组合模型，即如何将序列干预的效果分离为模块，从而阐明哪些数据条件允许我们在不同单元和时间步识别其组合效果。我们展示了我们组合模型的识别特性，其灵感来源于因果矩阵分解方法的进展。我们的重点在于针对新颖干预组合的预测模型，而非矩阵补全任务和因果效应估计。我们将我们的方法与灵活但通用的黑盒模型进行比较，以说明在稀疏数据条件下结构如何辅助预测。