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\begin{document}

\title{Quantifying Prediction Uncertainty in Regression using Random Fuzzy
Sets: the ENNreg model}



\author[1,1]{Thierry Denoeux }%
\affil[1]{Université de technologie de Compiègne}%


\vspace{-1em}



  
  \date{May 29, 2024}


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\begin{abstract}
We introduce a neural network model for regression in which prediction
uncertainty is quantified by Gaussian random fuzzy numbers (GRFNs), a
newly introduced family of random fuzzy subsets of the real line that
generalizes both Gaussian random variables and Gaussian possibility
distributions. The output GRFN is constructed by combining GRFNs induced
by prototypes using a combination operator that generalizes Dempster's
rule of Evidence Theory. The ~three output units indicate the most
plausible ~value of the response variable, variability around this
value, and epistemic uncertainty. The network is trained by minimizing a
loss function that generalizes the negative log-likelihood. Comparative
experiments show that this method is competitive, both in terms of
prediction accuracy and calibration error, with state-of-the-art
techniques such as random forests or deep learning with Monte Carlo
dropout. In addition, the model outputs a predictive belief function
that can be shown to be calibrated, in the sense that it allows us to
compute conservative prediction intervals with specified belief degree.%
\end{abstract}%



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