Beyond the Norms: Detecting Prediction Errors in Regression Models

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce the notion of unreliability in regression, i.e., when the output of the regressor exceeds a specified discrepancy (or error). Then, using powerful tools for probabilistic modeling, we estimate the discrepancy density, and we measure its statistical diversity using our proposed metric for statistical dissimilarity. In turn, this allows us to derive a data-driven score that expresses the uncertainty of the regression outcome. We show empirical improvements in error detection for multiple regression tasks, consistently outperforming popular baseline approaches, and contributing to the broader field of uncertainty quantification and safe machine learning systems. Our code is available at https: //zenodo.org/records/11281964 . This work aims to develop a simple yet effective framework to evaluate the reliability of the predictions of a given regressor and detect potentially anomalous situations that may arise. Our approach involves data-driven techniques to address the inherent challenges in the detection problem, particularly in compensating for estimation inaccuracies associated with baseline methods relying on the estimation of the conditional distribution of the dependent target variable. Contributions Our main contributions can be summarized as follows: 1. We study a novel detection challenge focused on identifying inaccuracies in the predictions made by a regres-