Semiparametric Inference for Counterfactual Regression under Intervention-Driven Shift

Abstract:We study counterfactual regression, which maps features to outcomes under hypothetical scenarios that differ from those observed in the data. This problem is central to decision-making under distribution shift, where treatment patterns may change at deployment. We develop a semiparametric framework for counterfactual regression along a prespecified incremental-intervention path. The target is a finite-dimensional constrained projection of counterfactual risk, estimated using cross-fitted influence-function representations of the program components. For smooth programs with fixed constraints and finite-dimensional programs with estimated linear constraints, we establish consistency and local stability of the optimizer under class-specific conditions, and derive pointwise and uniform first-order expansions. These results yield asymptotically valid inference, including simultaneous confidence bands for the counterfactual regression path. Simulations and an application to SMS reminders illustrate the finite-sample performance and practical applicability of the proposed approach.

Methodology (stat.ME); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2504.02694 [stat.ME]

(or arXiv:2504.02694v3 [stat.ME] for this version)

https://doi.org/10.48550/arXiv.2504.02694 Focus to learn more arXiv-issued DOI via DataCite

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