  One of the goals of causal inference is to generalize from past experiments
and observational data to novel conditions. While it is in principle possible
to eventually learn a mapping from a novel experimental condition to an outcome
of interest, provided a sufficient variety of experiments is available in the
training data, coping with a large combinatorial space of possible
interventions is hard. Under a typical sparse experimental design, this mapping
is ill-posed without relying on heavy regularization or prior distributions.
Such assumptions may or may not be reliable, and can be hard to defend or test.
In this paper, we take a close look at how to warrant a leap from past
experiments to novel conditions based on minimal assumptions about the
factorization of the distribution of the manipulated system, communicated in
the well-understood language of factor graph models. A postulated
$\textit{interventional factor model}$ (IFM) may not always be informative, but
it conveniently abstracts away a need for explicitly modeling unmeasured
confounding and feedback mechanisms, leading to directly testable claims. Given
an IFM and datasets from a collection of experimental regimes, we derive
conditions for identifiability of the expected outcomes of new regimes never
observed in these training data. We implement our framework using several
efficient algorithms, and apply them on a range of semi-synthetic experiments.
