\documentclass[accepted]{uai2024}

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% \title{Calibrated Propensity Scores \\for Causal Effect Estimation}

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\title{Calibrated and Conformal Propensity Scores for Causal Effect Estimation}

% The standard author block has changed for UAI 2024 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
% information below.
%
% Add authors
\author[1]{\href{mailto:<ssd86@cornell.edu>?Subject=Your UAI 2024 paper}{Shachi Deshpande}}
\author[1]{Volodymyr Kuleshov}
% Add affiliations after the authors
\affil[1]{%
    Dept of Computer Science\\
    Cornell University and Cornell Tech\\
    New York, NY, USA
}

  \begin{document}
  \maketitle
  
\begin{abstract}
Propensity scores are commonly used to
estimate treatment effects from observational data.
% balance observed covariates while estimating treatment effects. %Estimates obtained through propensity score weighing can be biased when the propensity score model cannot learn the true treatment assignment mechanism. 
We argue that the probabilistic output of a learned propensity score model should be calibrated---i.e., a predictive treatment probability of 90\% should correspond to 90\% individuals being assigned the treatment group---and we propose simple recalibration techniques to ensure this property. 
%We investigate the theoretical properties of a calibrated propensity score model and its role in unbiased treatment effect estimation. 
We prove that calibration is a necessary condition for unbiased treatment effect estimation when using popular inverse propensity weighted and doubly robust estimators. We derive error bounds on causal effect estimates that directly relate to the quality of uncertainties provided by the probabilistic propensity score model and show that calibration strictly improves this error bound while also avoiding extreme propensity weights. We demonstrate improved causal effect estimation with calibrated propensity scores in several tasks including high-dimensional image covariates and genome-wide association studies (GWASs). Calibrated propensity scores improve the speed of GWAS analysis by more than two-fold by enabling the use of simpler models that are faster to train. 
  
\end{abstract}




% The standard author block has changed for UAI 2023 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
% information below.
%
% Add authors

\input{src/introduction}
\input{src/background}


\input{src/calib_propensities}
\input{src/method}
\input{src/empirical}
\input{src/related}
\input{src/discussion}
% \input{src/conclusions}





% References
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\bibliography{bibliography}
% \input{src/checklist}
\input{src/appendix}

% \input{src/proof_ideas_updated}
\input{src/proof_ideas_submission}

\end{document}
