Outcome Assumptions and Duality Theory for Balancing Weights
This work addresses methodological improvements for causal inference and missing data estimation, offering incremental theoretical insights for researchers in statistics and machine learning.
The paper tackles the problem of estimating missing outcomes in a target population using balancing weight estimators by analyzing the implications of outcome model assumptions, showing that these assumptions simplify the optimization to a convex loss and replace overlap with a quantitative bias measure, while also demonstrating robustness under incorrect assumptions.
We study balancing weight estimators, which reweight outcomes from a source population to estimate missing outcomes in a target population. These estimators minimize the worst-case error by making an assumption about the outcome model. In this paper, we show that this outcome assumption has two immediate implications. First, we can replace the minimax optimization problem for balancing weights with a simple convex loss over the assumed outcome function class. Second, we can replace the commonly-made overlap assumption with a more appropriate quantitative measure, the minimum worst-case bias. Finally, we show conditions under which the weights remain robust when our assumptions on the outcomes are wrong.