Multi-Class Uncertainty Calibration via Mutual Information Maximization-based Binning
This work addresses the need for reliable confidence estimates in AI systems, particularly for safety-critical applications, by improving calibration without sacrificing accuracy, though it is incremental as it builds on existing binning methods.
The paper tackles the problem of multi-class calibration in deep neural networks, where existing methods either underestimate calibration error or harm classification accuracy, especially with small calibration sets. It proposes a new binning method based on mutual information maximization and a shared class-wise strategy, achieving state-of-the-art results on benchmarks like ImageNet with only 1k calibration samples.
Post-hoc multi-class calibration is a common approach for providing high-quality confidence estimates of deep neural network predictions. Recent work has shown that widely used scaling methods underestimate their calibration error, while alternative Histogram Binning (HB) methods often fail to preserve classification accuracy. When classes have small prior probabilities, HB also faces the issue of severe sample-inefficiency after the conversion into K one-vs-rest class-wise calibration problems. The goal of this paper is to resolve the identified issues of HB in order to provide calibrated confidence estimates using only a small holdout calibration dataset for bin optimization while preserving multi-class ranking accuracy. From an information-theoretic perspective, we derive the I-Max concept for binning, which maximizes the mutual information between labels and quantized logits. This concept mitigates potential loss in ranking performance due to lossy quantization, and by disentangling the optimization of bin edges and representatives allows simultaneous improvement of ranking and calibration performance. To improve the sample efficiency and estimates from a small calibration set, we propose a shared class-wise (sCW) calibration strategy, sharing one calibrator among similar classes (e.g., with similar class priors) so that the training sets of their class-wise calibration problems can be merged to train the single calibrator. The combination of sCW and I-Max binning outperforms the state of the art calibration methods on various evaluation metrics across different benchmark datasets and models, using a small calibration set (e.g., 1k samples for ImageNet).