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Whenever a binary classifier is used to provide decision support, it typically provides both a label prediction and a confidence value. Then, the decision maker is supposed to use the confidence value to calibrate how much to trust the prediction. In this context, it has been often argued that the confidence value should correspond to a well calibrated estimate of the probability that the predicted label matches the ground truth label. However, multiple lines of empirical evidence suggest that decision makers have difficulties at developing a good sense on when to trust a prediction using these confidence values. In this paper, our goal is first to understand why and then investigate how to construct more useful confidence values. We first argue that, for a broad class of utility functions, there exists data distributions for which a rational decision maker is, in general, unlikely to discover the optimal decision policy using the above confidence values—an optimal decision maker would need to sometimes place more (less) trust on predictions with lower (higher) confidence values. However, we then show that, if the confidence values satisfy a natural alignment property with respect to the decision maker’s confidence on her own predictions, there always exists an optimal decision policy under which the level of trust the decision maker would need to place on predictions is monotone on the confidence values, facilitating its discoverability. Further, we show that multicalibration with respect to the decision maker’s confidence on her own prediction is a sufficient condition for alignment. Experiments on a real AI-assisted decision making scenario where a classifier provides decision support to human decision makers validate our theoretical results and suggest that alignment may lead to better decisions.
Author Information
Nina Corvelo Benz (Max Planck Institute for Software Systems & ETH Zurich)
Manuel Gomez-Rodriguez (MPI-SWS)

Manuel Gomez Rodriguez is a faculty at Max Planck Institute for Software Systems. Manuel develops human-centric machine learning models and algorithms for the analysis, modeling and control of social, information and networked systems. He has received several recognitions for his research, including an outstanding paper award at NeurIPS’13 and a best research paper honorable mention at KDD’10 and WWW’17. He has served as track chair for FAT* 2020 and as area chair for every major conference in machine learning, data mining and the Web. Manuel has co-authored over 50 publications in top-tier conferences (NeurIPS, ICML, WWW, KDD, WSDM, AAAI) and journals (PNAS, Nature Communications, JMLR, PLOS Computational Biology). Manuel holds a BS in Electrical Engineering from Carlos III University, a MS and PhD in Electrical Engineering from Stanford University, and has received postdoctoral training at the Max Planck Institute for Intelligent Systems.
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