Structured Learning of Compositional Sequential Interventions

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 combinatorial sequences. 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 \emph{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 but focusing 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.