Hölder Bounds for Sensitivity Analysis in Causal Reasoning.

Assaad, Serge

Zeng, Shuxi

Pfister, Henry

Li, Fan

Carin, Lawrence

2021-08-19T23:05:01Z

2021-08-19T23:05:01Z

2021

2021-08-19T23:05:00Z

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.

https://hdl.handle.net/10161/23606

CoRR

cs.LG

cs.LG

cs.AI

stat.ML

Hölder Bounds for Sensitivity Analysis in Causal Reasoning.

Journal article

Pfister, Henry|0000-0001-5521-4397

Li, Fan|0000-0002-0390-3673

Trinity College of Arts & Sciences

Statistical Science

Biostatistics & Bioinformatics

Duke

Basic Science Departments

School of Medicine

Student

Electrical and Computer Engineering

Pratt School of Engineering

abs/2107.04661