Generalized Neural Distributional Regression

• URL: http://arxiv.org/abs/2607.14122v1
• Date: Tue, 16 Jun 2026 19:01:57 GMT
• Title: Generalized Neural Distributional Regression
• Abstract summary: We introduce the Generalized Neural Distributional Regression (GNDR) framework, which seamlessly embeds deep neural networks into the space of classical probability distributions.<n>We demonstrate the framework's versatility and superior distributional calibration across diverse modalities, including overdispersed clinical counts, right-ed transcriptomic survival profiles under a cure, and zero-truncated age distributions from unstructured facial images.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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