  Causal inference of exact individual treatment outcomes in the presence of
hidden confounders is rarely possible. Recent work has extended prediction
intervals with finite-sample guarantees to partially identifiable causal
outcomes, by means of a sensitivity model for hidden confounding. In deep
learning, predictors can exploit their inductive biases for better
generalization out of sample. We argue that the structure inherent to a deep
ensemble should inform a tighter partial identification of the causal outcomes
that they predict. We therefore introduce an approach termed Caus-Modens, for
characterizing causal outcome intervals by modulated ensembles. We present a
simple approach to partial identification using existing causal sensitivity
models and show empirically that Caus-Modens gives tighter outcome intervals,
as measured by the necessary interval size to achieve sufficient coverage. The
last of our three diverse benchmarks is a novel usage of GPT-4 for
observational experiments with unknown but probeable ground truth.
