Belted Engression：生成式分布回归的充分降维
Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression
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中文总结 AI 辅助
针对条件生成模型学习复杂协变量依赖的挑战，提出Belted Engression框架，通过嵌入结构瓶颈实现端到端压缩-生成，理论上证明SDR等价性并给出更优收敛速率，实验表明以更少参数取得更优分布预测与降维恢复。
中文摘要 AI 辅助
现代条件生成模型在学习复杂协变量依赖关系时面临重大挑战。虽然充分降维（SDR）为压缩这些依赖关系提供了一种原则性方法，但传统的SDR框架并非为条件生成而设计。为弥合这一差距，我们提出了Belted Engression，一个用于生成式分布回归的统一且架构参数高效的框架。我们的方法建立了一种由充分表示学习驱动的端到端“先压缩后生成”范式，将结构瓶颈嵌入生成架构中。理论上，我们证明了标准SDR条件等价于一种保律生成分解，该分解在总体Belted Engression目标函数的全局最优处实现。此外，通过揭示能量分数损失的局部Bernstein型控制，我们建立了比现有结果更锐利的有限样本收敛速率。我们还证明了这种带式架构严格更小，其参数数量相对于无结构基线渐近趋于零。大量模拟和实际应用表明，Belted Engression以更少的可训练参数实现了更优的分布预测和SDR恢复。
英文摘要
Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.
发表机构
- The Pennsylvania State University（宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。
