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This paper offers a rigorous theoretical breakdown of error sources in neural-network-based engression, decomposing excess risk into approximation, stochastic, and Monte Carlo components to establish convergence rates for generative modeling under energy scores. By formalizing the smoothness assumptions required for these deep learning approaches, it provides essential insights for researchers developing robust probabilistic machine learning models rather than focusing on immediate product applications or consumer impacts.
Error Analysis of Neural-Network-Based Engression
arXiv:2607.27723v1 Announce Type: cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG); Methodology (stat.ME)
arXiv:2607.27723 [stat.ML]
(or arXiv:2607.27723v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2607.27723 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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