[2503.12354] Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions

Computer Science > Machine Learning arXiv:2503.12354 (cs) [Submitted on 16 Mar 2025 (v1), last revised 26 Feb 2026 (this version, v2)] Title:Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions Authors:Farhad Pourkamali-Anaraki View a PDF of the paper titled Probabilistic Neural Networks (PNNs) with t-Distributed Outputs: Adaptive Prediction Intervals Beyond Gaussian Assumptions, by Farhad Pourkamali-Anaraki View PDF HTML (experimental) Abstract:Traditional neural network regression models provide only point estimates, failing to capture predictive uncertainty. Probabilistic neural networks (PNNs) address this limitation by producing output distributions, enabling the construction of prediction intervals. However, the common assumption of Gaussian output distributions often results in overly wide intervals, particularly in the presence of outliers or deviations from normality. To enhance the adaptability of PNNs, we propose t-Distributed Neural Networks (TDistNNs), which generate t-distributed outputs, parameterized by location, scale, and degrees of freedom. The degrees of freedom parameter allows TDistNNs to model heavy-tailed predictive distributions, improving robustness to non-Gaussian data and enabling more adaptive uncertainty quantification. We incorporate a likelihood based on the t-distribution into neural network training and derive efficient gradient computations for seamless integration into...