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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.
|Title of host publication||Advances in Neural Information Processing Systems 32 (NIPS 2019)|
|Editors||Hannah Wallach, Hugo Larochelle, Alina Beygelzimer, Florence d'Alché-Buc, Emily Fox, Roman Garnett|
|Publisher||Neural Information Processing Systems Foundation|
|Number of pages||12|
|Publication status||Accepted/In press - 3 Sep 2019|
- Digital Health
Kull, M., Perello Nieto, M., Kängsepp, M., Silva Filho, T., Song, H., & Flach, P. (Accepted/In press). Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, & R. Garnett (Eds.), Advances in Neural Information Processing Systems 32 (NIPS 2019) Neural Information Processing Systems Foundation.