Error Analysis of Neural-Network-Based Engression
arXiv:2607.27723
The paper analyzes the theoretical error of neural‑network‑based engression, a method for learning conditional distributions via an energy score, and derives convergence rates by decomposing excess risk into approximation, stochastic, and Monte Carlo components.
Abstract
Engression (Shen and Meinshausen, 2024) learns a conditional distribution by fitting a generative model 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.
37 pages, 1 figure