发表机构
School of Mathematical Sciences, Xiamen University; Center for Data Science, Zhejiang University; Department of Statistics, University of Washington（厦门大学数学科学学院; 浙江大学数据科学中心; 华盛顿大学统计系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对深度神经网络实现的Engression开展理论误差分析，分解超额风险为三类误差，在特定假设下建立其收敛速率。
AI 中文摘要
Engression（Shen和Meinshausen，2024）通过在严格适当计分规则能量得分下拟合生成模型$Y = f(X,\varepsilon)$来学习条件分布。本文对用深度神经网络实现的Engression进行理论误差分析，将超额风险分解为近似误差、随机误差和蒙特卡洛误差三部分，基于此在目标条件生成器具有组合光滑性结构的假设下建立收敛速率。
英文摘要
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.
Comments37 pages, 1 figure
