Generalized Neural Distributional Regression

Natan Hilario da Silva; Vicente Garibay Cancho; Adriano Kamimura Suzuki

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arXiv · 2607.14122

Generalized Neural Distributional Regression

Natan Hilario da Silva·Vicente Garibay Cancho·Adriano Kamimura Suzuki

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Abstract

We introduce the Generalized Neural Distributional Regression (GNDR) framework, which seamlessly embeds deep neural networks into the parameter space of classical probability distributions. To reconcile the inherent non-identifiability of deep architectures with maximum likelihood theory, we propose a two-step semi-parametric estimation procedure. By isolating the terminal prediction heads and treating the upstream network as a fixed, non-linear basis expansion, GNDR enables the extraction of analytical Fisher Information matrices. This facilitates rigorous uncertainty quantification, generating observation-specific confidence bands and tolerance intervals via the multivariate Delta method. We demonstrate the framework's versatility and superior distributional calibration across diverse data modalities, including overdispersed clinical counts, right-censored transcriptomic survival profiles under a mixture cure framework, and zero-truncated age distributions derived directly from unstructured facial images. The methodology is natively implemented in the open-source Python package \textit{thetaflow}.

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Natan Hilario da Silva, Vicente Garibay Cancho, Adriano Kamimura Suzuki. 2026-06-16. Generalized Neural Distributional Regression. https://arxiv.org/abs/2607.14122

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