  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.
