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Beyond temperature scaling: Obtaining well-calibrated multi-class probabilities with Dirichlet calibration
Meelis Kull · Miquel Perello Nieto · Markus Kängsepp · Telmo Silva Filho · Hao Song · Peter Flach

Wed Dec 11 10:45 AM -- 12:45 PM (PST) @ East Exhibition Hall B + C #38

Class probabilities predicted by most multiclass classifiers are uncalibrated, often tending towards over-confidence. With neural networks, calibration can be improved by temperature scaling, a method to learn a single corrective multiplicative factor for inputs to the last softmax layer. On non-neural models the existing methods apply binary calibration in a pairwise or one-vs-rest fashion. We propose a natively multiclass calibration method applicable to classifiers from any model class, derived from Dirichlet distributions and generalising the beta calibration method from binary classification. It is easily implemented with neural nets since it is equivalent to log-transforming the uncalibrated probabilities, followed by one linear layer and softmax. Experiments demonstrate improved probabilistic predictions according to multiple measures (confidence-ECE, classwise-ECE, log-loss, Brier score) across a wide range of datasets and classifiers. Parameters of the learned Dirichlet calibration map provide insights to the biases in the uncalibrated model.

Author Information

Meelis Kull (University of Tartu)
Miquel Perello Nieto (University of Bristol)
Markus Kängsepp (University of Tartu)

I am a doctorate student interested in machine learning, especially in deep learning and context-aware learning.

Telmo Silva Filho (Universidade Federal da Paraíba)
Hao Song (University of Bristol)
Peter Flach (University of Bristol)

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