Do you understand epistemic uncertainty? Think again! Rigorous frequentist epistemic uncertainty estimation in regression

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a novel frequentist approach to epistemic and aleatoric uncertainty estimation. We train models to generate conditional predictions by feeding their initial output back as an additional input. This method allows for a rigorous measurement of model uncertainty by observing how prediction responses change when conditioned on the model's previous answer. We provide a complete theoretical framework to analyze epistemic uncertainty in regression in a frequentist way, and explain how it can be exploited in practice to gauge a model's uncertainty, with minimal changes to the original architecture.

Active Learning for Regression based on Wasserstein distance and GroupSort Neural Networks

This paper addresses a new active learning strategy for regression problems. The presented Wasserstein active regression model is based on the principles of distribution-matching to measure the representativeness of the labeled dataset. The Wasserstein distance is computed using GroupSort Neural Networks. The use of such networks provides theoretical foundations giving a way to quantify errors with explicit bounds for their size and depth. This solution is combined with another uncertainty-based approach that is more outlier-tolerant to complete the query strategy. Finally, this method is compared with other classical and recent solutions. The study empirically shows the pertinence of such a representativity-uncertainty approach, which provides good estimation all along the query procedure. Moreover, the Wasserstein active regression often achieves more precise estimations and tends to improve accuracy faster than other models.