Error Analysis of Neural-Network-Based Engression
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Abstract (arXiv)
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.
Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 10 of its 38 references that are in the map. First posted on arXiv 30 Jul 2026.
Builds on
10 of 38 references.
References · 10
- 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
- 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
- 2022Do Bayesian Neural Networks Need To Be Fully Stochastic?cited by 63
- 2023Engression: Extrapolation through the Lens of Distributional Regressioncited by 49
- 2021An error analysis of generative adversarial networks for learning distributionscited by 35
- 2023Wasserstein Generative Regressioncited by 12
- 2022Distributional regression and its evaluation with the CRPS: Bounds and convergence of the minimax riskcited by 3
- 2026Theoretical Analysis of Engression and Reverse Markov Engressioncited by 3
- 2026Neural Generative Distributional Regressioncited by 2
- 2026Semi-Supervised Learning on Graphs using Graph Neural Networkscited by 1
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Citing papers per year: 2026: 3.
3 papers.