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%\newcommand{\ourtitle}{Evaluating Decision Makers over Selectively Labeled Data}


%\newcommand{\ourtitle}{A Causal Approach to\\Evaluating Decision Makers over Selectively Labeled Data}

\newcommand{\ourtitle}{Evaluating Decision Makers over Selectively Labeled Data:\\
A Causal Modeling Approach
}

% A in the Presence of Unobservables and Selective Labels
% A Causal Treatment for Unobservables and Selective Labels
% Incomplete Data
%-unobservables
%-selective labels

%-causal
%-bayesian


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\title{\ourtitle}

%\author{Michael Mathioudakis}
%\affiliation{%
 % \institution{University of Helsinki}
 % \city{Helsinki} 
 % \country{Finland} 
%}
%\email{michael.mathioudakis@helsinki.fi}


\begin{abstract}
Today, AI systems replace humans in an increasing number of decisions affecting people's lives.
%
Therefore, it is important to evaluate the performance of such systems {\it offline}, i.e., before they are deployed in real settings --
and compare it to the performance of human decisions they aim to replace.
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The data which such evaluation is performed on has two major challenges, biasing any direct evaluations of considered decision makers.
%
First, in most cases the data does not include all factors that play a role in the decisions recorded in it.
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Second, the past decision in the data skew the data, and, in particular, any possible outcomes recorded in it.
%Another major challenge in such cases is that often past decisions have skewed the data on which the evaluation is performed. 
%
For example, when a bank decides whether a customer should be granted a loan, it is desired to grant loans to customers who would honor its conditions, but not to ones who would violate them.
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However, we can directly evaluate only the decision to grant the loan, while we cannot observe whether customers who were not granted the loan would indeed violate its conditions. 
%
%THIS IS NOT SKEW THIS IS MISSING DATA
% 
Such selection bias appears in the decisions of both human and AI decision makers -- and should be properly taken into account for evaluation.
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%Further complications arise since commonly not all features that the decisions are based on are observed. DISCUSS UNOBSERVABLES IN THE INTRO?
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In this paper, we develop a Bayesian approach towards this end, using what we call counterfactual-based imputation.
% to infer unobserved outcomes.
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Compared to previous state-of-the-art, the quality of decisions is estimated more accurately and with lower variance. 
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The approach is also %demonstrated to be 
robust to different variations in the decision mechanisms in the data.
%
\end{abstract}


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\input{setting}

\input{imputation}

\input{experiments} 

\input{related} 

\input{conclusions}


% \textbf{Acknowledgments.}
%The computational resources must be mentioned. 

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\input{appendix}

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