Taking a Step Back with KCal: Multi-Class Kernel-Based Calibration for Deep Neural Networks

Deep neural network (DNN) classifiers are often overconfident, producing miscalibrated class probabilities. Most existing calibration methods either lack theoretical guarantees for producing calibrated outputs or reduce the classification accuracy in the process. This paper proposes a new Kernel-based calibration method called KCal. Unlike other calibration procedures, KCal does not operate directly on the logits or softmax outputs of the DNN. Instead, it uses the penultimate-layer latent embedding to train a metric space in a supervised manner. In effect, KCal amounts to a supervised dimensionality reduction of the neural network embedding, and generates a prediction using kernel density estimation on a holdout calibration set. We first analyze KCal theoretically, showing that it enjoys a provable asymptotic calibration guarantee. Then, through extensive experiments, we confirm that KCal consistently outperforms existing calibration methods in terms of both the classification accuracy and the (confidence and class-wise) calibration error.