基于 ReLU 神经网络的任意响应变量分布回归框架
Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks
这篇论文把分布回归推广到任意响应变量，用 DAG 约束保证预测一致性，还给出了 ReLU 网络的显式收敛速率，做统计学习理论的可以看看。
arXiv 论文 2610.16142 提出一个统一的分布回归框架，将响应变量从标量阈值扩展到可测集定义的条件事件概率。框架包含两个估计器：基于事件指标独立回归的初步估计器，以及通过有向无环图（DAG）约束保证包含一致性的约束估计器。作者为两个估计器建立了一般误差界，并针对稠密 ReLU 网络给出显式收敛速率，克服维度灾难。仿真和真实数据实验验证了方法的有效性。
Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks
This paper develops a unified framework for distributional regression with arbitrary response variables. Rather than relying on scalar thresholds or Euclidean structure, we model conditional event probabilities indexed by measurable sets, which extends distributional regression to general response spaces while retaining a direct connection to classical event-based formulations. Within this framework, we study two complementary estimators: a preliminary estimator based on separate regression of event indicators, and a constrained estimator that enforces inclusion-consistent predictions through a directed acyclic graph (DAG) over a finite set family. We establish general error bounds for both estimators and further specialize the results to dense ReLU networks, yielding explicit convergence rates overcoming the curse of dimensionality. Simulation studies and real-data experiments further demonstrate the practical effectiveness of the proposed framework.
