广义神经分布回归
Generalized Neural Distributional Regression
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中文总结 AI 辅助
介绍广义神经分布回归框架，提出两步半参数估计程序，通过特定方式提取信息矩阵以进行不确定性量化，在多种数据模式下展现通用性和分布校准优势，且在开源包中实现。
中文摘要 AI 辅助
我们引入了广义神经分布回归（GNDR）框架，它将深度神经网络无缝嵌入经典概率分布的参数空间。为使深度架构的固有不可识别性与最大似然理论协调，我们提出两步半参数估计程序。通过分离终端预测头并将上游网络视为固定的非线性基展开，GNDR能提取解析Fisher信息矩阵，便于严格的不确定性量化。我们在多种数据模式下展示了该框架的通用性和卓越的分布校准。该方法在开源Python包thetaflow中实现。
英文摘要
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}.
发表机构
- Federal University of São Carlos, University of São Paulo（巴西圣保罗联邦大学、圣保罗大学）
- Institute of Mathematics and Computer Sciences, University of São Paulo（圣保罗大学数学与计算机科学学院）
机构由 AI 辅助整理，请以论文原文为准。
