Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration
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When facing uncertainty, decision-makers want predictions they can trust. A machine learning provider can convey confidence to decision-makers by guaranteeing their predictions are distribution calibrated – amongst the inputs that receive a predicted class probabilities vector q, the actual distribution over classes is q. For multi-class prediction problems, however, achieving distribution calibration tends to be infeasible, requiring sample complexity exponential in the number of classes C. In this work, we introduce a new notion – decision calibration – that requires the predicted distribution and true distribution to be “indistinguishable” to a set of downstream decision-makers. When all possible decision makers are under consideration, decision calibration is the same as distribution calibration. However, when we only consider decision makers choosing between a bounded number of actions (e.g. polynomial in C), our main result shows that decisions calibration becomes feasible – we design a recalibration algorithm that requires sample complexity polynomial in the number of actions and the number of classes. We validate our recalibration algorithm empirically: compared to existing methods, decision calibration improves decision-making on skin lesion and ImageNet classification with modern neural network predictors.
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