将神经网络嵌入概率分布参数空间，实现精准不确定性量化。
Generalized Neural Distributional Regression
- 用两步半参数法分离网络特征与预测头，解决深度模型不可识别性问题。
- 可计算解析的Fisher信息矩阵，生成个体化置信带和容许区间。
- 适用于临床计数、生存分析、人脸年龄估计等多类数据，效果优于传统方法。
我们提出广义神经分布回归（GNDR）框架，将深度神经网络无缝嵌入经典概率分布的参数空间。为调和深度架构的固有非唯一性与最大似然理论之间的矛盾，提出两步半参数估计方法。通过将末端预测头独立出来，并将上游网络视为固定的非线性基函数展开，GNDR 可提取解析的 Fisher 信息矩阵，从而通过多元 Delta 方法实现严格的不确定性量化，生成基于观测值的置信带与容许区间。我们在多种数据模态上验证了该框架的通用性与优越的分布校准能力，包括过分散的临床计数数据、混合治愈框架下的右删失转录组生存数据，以及直接从非结构化人脸图像中提取的零截断年龄分布。该方法已开源集成于 Python 包 thetaflow。
原文摘要 · Abstract (English)
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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