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Uncertainty Quantification in Neural Networks for Latent-Driven Non-Gaussian Outputs

Year: 2026
Type: article
Abstract: Uncertainty quantification (UQ) is essential for reliable predictions in artificial neural networks when latent sources of randomness produce non-Gaussian outputs for a given deterministic input. We propose UQ-ANN, a data-driven framework composed of two coupled subnetworks. The first subnetwork contains two feedforward neural networks: ANN1 predicts the conditional mean and ANN2 the conditional covariance of a reduced representation obtained by principal component analysis (PCA) of the outputs. The second subnetwork is an analytical stochastic generator and requires no training. It is based on a sparse Gaussian kernel density estimator (GKDE) constructed by adaptive clustering. The sparsification replaces the kernels associated with the training points by a reduced set of cluster-based kernels, while third- and fourth-moment descriptors are included in the merging criterion to preserve non-Gaussian features. Independent realizations in the reduced space are then generated, transformed to reproduce the conditional mean and covariance predicted by the first subnetwork, and mapped back to the original output space. They provide conditional statistics, conditional probability density functions, and conditional prediction intervals. A marginal log-density diagnostic is also used to assess the stochastic approximation. Numerical tests on synthetic datasets evaluate the sparse GKDE, the stochastic generator, and the complete UQ-ANN framework, including out-of-sample predictions.
DOI: 10.3390/modelling7050220
Language: English
Open Access status: gold
Estimated APC paid: $1,207
OpenAlex ID: W7221329151
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