Uncertainty quantification in regression neural networks using evidential likelihood-based inference

We introduce a new method for quantifying prediction uncertainty in regression neural networks using evidential likelihood-based inference. The method is based on the Gaussian approximation of the likelihood function and the linearization of the network output with respect to the weights. Prediction uncertainty is described by a random fuzzy set inducing a predictive belief function. Two models are considered: a simple one with constant conditional variance and a more complex one in which the conditional variance is predicted by an auxiliary neural network. Both models are trained by regularized log-likelihood maximization using a standard optimization algorithm. The postprocessing required for uncertainty quantification only consists of one computation and inversion of the Hessian matrix after convergence. Numerical experiments show that the approximations are quite accurate and that the method allows for conservative uncertainty-aware predictions.