H\"older Bounds for Sensitivity Analysis in Causal Reasoning
Abstract
We examine interval estimation of the effect of a treatment T on an outcome Y given the existence of an unobserved confounder U. Using H\"older's inequality, we derive a set of bounds on the confounding bias |E[Y|T=t]-E[Y|do(T=t)]| based on the degree of unmeasured confounding (i.e., the strength of the connection U->T, and the strength of U->Y). These bounds are tight either when U is independent of T or when U is independent of Y given T (when there is no unobserved confounding). We focus on a special case of this bound depending on the total variation distance between the distributions p(U) and p(U|T=t), as well as the maximum (over all possible values of U) deviation of the conditional expected outcome E[Y|U=u,T=t] from the average expected outcome E[Y|T=t]. We discuss possible calibration strategies for this bound to get interval estimates for treatment effects, and experimentally validate the bound using synthetic and semi-synthetic datasets.
Keywords
Cite
@article{arxiv.2107.04661,
title = {H\"older Bounds for Sensitivity Analysis in Causal Reasoning},
author = {Serge Assaad and Shuxi Zeng and Henry Pfister and Fan Li and Lawrence Carin},
journal= {arXiv preprint arXiv:2107.04661},
year = {2021}
}
Comments
Workshop on the Neglected Assumptions in Causal Inference at the International Conference on Machine Learning (ICML), 2021