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Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks

  • Junpeng Ren
  • Carlos Misael Madrid Padilla
  • Oscar Hernan Madrid Padilla
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{ren2026distributional,
  title = {{Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks}},
  author = {Junpeng Ren and Carlos Misael Madrid Padilla and Oscar Hernan Madrid Padilla},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16142},
  eprint = {2610.16142},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16142},
}
RIS
TY  - UNPB
TI  - Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks
AU  - Junpeng Ren
AU  - Carlos Misael Madrid Padilla
AU  - Oscar Hernan Madrid Padilla
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16142
UR  - https://arxiv.org/abs/2610.16142
AB  - 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.
ER  -