Multivariate Deep Evidential Regression

TL;DR

This paper introduces a multivariate deep evidential regression method that enables neural networks to estimate both aleatoric and epistemic uncertainties directly from data, improving uncertainty quantification in safety-critical applications.

Contribution

It extends evidential neural network techniques to multivariate regression, providing a principled way to extract uncertainties without sampling or out-of-distribution data.

Findings

Effective uncertainty estimation for multivariate regression

Avoids sampling and out-of-distribution data

Addresses theoretical and implementation gaps

Abstract

There is significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, yet several important gaps in the theory and implementation of these networks remain. We discuss three issues with a proposed solution to extract aleatoric and epistemic uncertainties from regression-based neural networks. The approach derives a technique by placing evidential priors over the original Gaussian likelihood function and training the NN to infer the hyperparameters of the evidential distribution. Doing so allows for the simultaneous extraction of both uncertainties without sampling or utilization of out-of-distribution data for univariate regression tasks. We describe the outstanding issues in detail, provide a possible solution, and generalize the deep evidential regression technique for multivariate cases.