Integer Programming for Generalized Causal Bootstrap Designs

2024-10-28

AI Summary

In experimental causal inference, design uncertainty—arising from the assignment mechanism—is often overlooked under small sample sizes and heterogeneous treatment effects; conventional causal bootstrap methods apply only to completely randomized designs and average treatment effect estimation. This paper addresses this limitation by introducing integer linear programming into the causal bootstrap framework for the first time, enabling computation of the worst-case copula under generalized assignment mechanisms (e.g., conditional unconfoundedness, bounded confounding) to uniformly calibrate design uncertainty. The method accommodates both linear and quadratic treatment effect estimators and is supported by asymptotic theory establishing its validity. Monte Carlo simulations demonstrate that, in small-scale geographic experiments, the proposed approach substantially improves confidence interval coverage and precision while delivering more robust control of Type I error.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In experimental causal inference, we distinguish between two sources of uncertainty: design uncertainty, due to the treatment assignment mechanism, and sampling uncertainty, when the sample is drawn from a super-population. This distinction matters in settings with small fixed samples and heterogeneous treatment effects, as in geographical experiments. The standard bootstrap procedure most often used by practitioners primarily estimates sampling uncertainty, and the causal bootstrap procedure, which accounts for design uncertainty, was developed for the completely randomized design and the difference-in-means estimator, whereas non-standard designs and estimators are often used in these low-power regimes. We address this gap by proposing an integer program which computes numerically the worst-case copula used as an input to the causal bootstrap method, in a wide range of settings. Specifically, we prove the asymptotic validity of our approach for unconfounded, conditionally unconfounded, and and individualistic with bounded confoundedness assignments, as well as generalizing to any linear-in-treatment and quadratic-in-treatment estimators. We demonstrate the refined confidence intervals achieved through simulations of small geographical experiments.

Problem

• Extends causal bootstrap to non-standard designs and estimators
• Addresses design uncertainty in small fixed heterogeneous samples
• Generalizes method for various assignment types and estimators

Innovation

• Integer programming for worst-case copula computation
• Generalizes causal bootstrap to non-standard designs
• Valid for various assignment types and estimators