Quantile Regularization: Towards Implicit Calibration of Regression Models
This addresses the issue of unreliable predictive uncertainty estimates in regression models for machine learning practitioners, offering a novel training-based solution rather than incremental post-hoc adjustments.
The paper tackles the problem of poor calibration in regression models by introducing a quantile regularizer that enables end-to-end training without needing an additional dataset, achieving significantly better calibration compared to post-hoc methods like Isotonic Calibration.
Recent works have shown that most deep learning models are often poorly calibrated, i.e., they may produce overconfident predictions that are wrong. It is therefore desirable to have models that produce predictive uncertainty estimates that are reliable. Several approaches have been proposed recently to calibrate classification models. However, there is relatively little work on calibrating regression models. We present a method for calibrating regression models based on a novel quantile regularizer defined as the cumulative KL divergence between two CDFs. Unlike most of the existing approaches for calibrating regression models, which are based on post-hoc processing of the model's output and require an additional dataset, our method is trainable in an end-to-end fashion without requiring an additional dataset. The proposed regularizer can be used with any training objective for regression. We also show that post-hoc calibration methods like Isotonic Calibration sometimes compound miscalibration whereas our method provides consistently better calibrations. We provide empirical results demonstrating that the proposed quantile regularizer significantly improves calibration for regression models trained using approaches, such as Dropout VI and Deep Ensembles.