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# Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding

*Proceedings of the Third Conference on Causal Learning and Reasoning*, PMLR 236:18-40, 2024.

#### Abstract

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**caus**al outcome intervals by**mod**ulated**ens**embles. 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.