An Evidential Neural Network Model for Regression Based on Random Fuzzy Numbers
This work addresses uncertainty quantification in regression for machine learning practitioners, presenting an incremental improvement by combining existing concepts in a novel way.
The paper tackles regression by introducing a neural network model that quantifies prediction uncertainty using belief functions based on random fuzzy numbers, achieving very good performance compared to state-of-the-art evidential and statistical learning algorithms in experiments with real datasets.
We introduce a distance-based neural network model for regression, in which prediction uncertainty is quantified by a belief function on the real line. The model interprets the distances of the input vector to prototypes as pieces of evidence represented by Gaussian random fuzzy numbers (GRFN's) and combined by the generalized product intersection rule, an operator that extends Dempster's rule to random fuzzy sets. The network output is a GRFN that can be summarized by three numbers characterizing the most plausible predicted value, variability around this value, and epistemic uncertainty. Experiments with real datasets demonstrate the very good performance of the method as compared to state-of-the-art evidential and statistical learning algorithms. \keywords{Evidence theory, Dempster-Shafer theory, belief functions, machine learning, random fuzzy sets.