ArXiv

Error Analysis of Neural-Network-Based Engression

2026-07-30 · 05:59 UTC ·Juntong Chen, Zijian Guo, Xinwei Shen ·0 min read
Authors
Juntong Chen, Zijian Guo, Xinwei Shen
Categories
stat.ML, cs.LG, stat.ME
arXiv
https://arxiv.org/abs/2607.27723v1
PDF
https://arxiv.org/pdf/2607.27723v1

Brief

Neural-network-based engression — fitting a generator Y = f(X, ε) under the energy score (Shen & Meinshausen, 2024) — is analyzed theoretically: the authors decompose the excess risk into approximation, stochastic, and Monte Carlo components and establish convergence rates assuming the true conditional generator has a compositional smoothness structure. Summary is based on the abstract; full text was not reviewed.

Why it matters

Provides a theoretical error analysis for neural-network-based engression (building on Shen & Meinshausen, 2024), decomposing the excess risk into three terms: approximation error, stochastic error, and Monte Carlo error.

Key details

  • Derives convergence rates under the assumption that the target conditional generator admits a compositional smoothness structure; fitting is done by learning a generator Y = f(X, ε) with the energy score (a strictly proper scoring rule).
  • ArXiv preprint by Juntong Chen, Zijian Guo, and Xinwei Shen (posted 2026-07-30); 37 pages and 1 figure (PDF available at https://arxiv.org/pdf/2607.27723v1).
Source evidence

Abstract

Engression (Shen and Meinshausen, 2024) learns a conditional distribution by fitting a generative model $Y = f(X,\varepsilon)$ under the energy score, a strictly proper scoring rule. We provide a theoretical error analysis of engression implemented with deep neural networks. We decompose the excess risk into three components: the approximation error, the stochastic error, and the Monte Carlo error. Based on this decomposition, we establish convergence rates under the assumption that the target conditional generator admits a compositional smoothness structure.

Comment: 37 pages, 1 figure