Hölder 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.
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Scholars@Duke
Serge Assaad
Henry Pfister
Henry D. Pfister received his Ph.D. in Electrical Engineering in 2003 from the University of California, San Diego and is currently a professor in the Electrical and Computer Engineering Department of Duke University with a secondary appointment in Mathematics. Prior to that, he was an associate professor at Texas A&M University (2006-2014), a post-doctoral fellow at the École Polytechnique Fédérale de Lausanne (2005-2006), and a senior engineer at Qualcomm Corporate R&D in San Diego (2003-2004). His current research interests include information theory, error-correcting codes, quantum computing, and machine learning.
He received the NSF Career Award in 2008 and a Texas A&M ECE Department Outstanding Professor Award in 2010. He is a coauthor of the 2007 IEEE COMSOC best paper in Signal Processing and Coding for Data Storage and a coauthor of a 2016 Symposium on the Theory of Computing (STOC) best paper. He has served the IEEE Information Theory Society as a member of the Board of Governors (2019-2022), an Associate Editor for the IEEE Transactions on Information Theory (2013-2016), and a Distinguished Lecturer (2015-2016). He was also the General Chair of the 2016 North American School of Information Theory.
Fan Li
My main research interest is causal inference and its applications to health, policy and social science. I also work on the interface between causal inference and machine learning. I have developed methods for propensity score, clinical trials, randomized experiments (e.g. A/B testing), difference-in-differences, regression discontinuity designs, representation learning. I also work on Bayesian analysis and statistical methods for missing data. I am serving as the editor for social science, biostatistics and policy for the journal Annals of Applied Statistics.
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