Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration

• URL: http://arxiv.org/abs/2107.05719v1
• Date: Mon, 12 Jul 2021 20:17:28 GMT
• Title: Calibrating Predictions to Decisions: A Novel Approach to Multi-Class Calibration
• Authors: Shengjia Zhao, Michael P. Kim, Roshni Sahoo, Tengyu Ma, Stefano Ermon
• Abstract summary: We introduce a new notion -- emphdecision calibration -- that requires the predicted distribution and true distribution to be indistinguishable'' to a set of downstream decision-makers. Decision calibration improves decision-making on skin lesions and ImageNet classification with modern neural network.
• Score: 118.26862029820447
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 -- \emph{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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