A Large-Scale Study of Probabilistic Calibration in Neural Network Regression

TL;DR

This paper conducts the largest empirical study on neural network calibration in regression, analyzing various methods and introducing novel techniques to improve probabilistic predictions.

Contribution

It provides a comprehensive evaluation of calibration methods in neural network regression and introduces new differentiable recalibration and regularization techniques.

Findings

Regularization offers a good balance between calibration and sharpness.

Post-hoc methods achieve better calibration due to conformal prediction guarantees.

Quantile recalibration is a special case of conformal prediction.

Abstract

Accurate probabilistic predictions are essential for optimal decision making. While neural network miscalibration has been studied primarily in classification, we investigate this in the less-explored domain of regression. We conduct the largest empirical study to date to assess the probabilistic calibration of neural networks. We also analyze the performance of recalibration, conformal, and regularization methods to enhance probabilistic calibration. Additionally, we introduce novel differentiable recalibration and regularization methods, uncovering new insights into their effectiveness. Our findings reveal that regularization methods offer a favorable tradeoff between calibration and sharpness. Post-hoc methods exhibit superior probabilistic calibration, which we attribute to the finite-sample coverage guarantee of conformal prediction. Furthermore, we demonstrate that quantile recalibration can be considered as a specific case of conformal prediction. Our study is fully reproducible and implemented in a common code base for fair comparisons.