用可复用的去噪模型加速高维依赖建模，提升密度与信息估计效率。
Amortized Vine Copulas for High-Dimensional Density and Information Estimation
- 训练一个通用双变量去噪模型，复用于所有藤结构边。
- 通过投影使边缘分布均匀化，保持藤结构似然可计算性。
- 在真实与合成数据上实现快速高维拟合，适合需重复建模的场景。
高维依赖关系建模同时保持似然可计算性仍具挑战：传统藤结构耦合方法可解释但代价高，许多神经估计器灵活却缺乏结构。本文提出藤结构去噪耦合器（VDC），一种针对连续数据的简化藤结构依赖建模的摊销式藤结构耦合器。VDC仅需训练一个双变量去噪模型，并将其复用于所有藤结构边。每条边上，给定伪观测值，模型预测分段常数密度网格，再通过IPFP/Sinkhorn投影归一化质量并驱动边缘分布趋于均匀。该方法保留了可计算的藤结构似然结构和标准耦合解释，将重复的逐边优化替换为GPU推理。在合成与真实数据基准测试中，VDC表现出优异的双变量密度精度，具有竞争力的互信息与总相关性估计能力，且高维藤结构拟合速度显著提升。这些优势使得在重复藤结构拟合成本过高的情况下，显式信息估计与依赖分解成为可能，但条件下游任务仍是局限。
原文摘要 · Abstract (English)
Modeling high-dimensional dependencies while keeping likelihoods tractable remains challenging. Classical vine-copula pipelines are interpretable but can be expensive, while many neural estimators are flexible but less structured. In this work, we propose Vine Denoising Copula (VDC), an amortized vine-copula pipeline for continuous-data, simplified-vine dependence modeling. VDC trains a single bivariate denoising model and reuses it across all vine edges. For each edge, given pseudo-observations, the model predicts a piecewise-constant density grid. We then apply an IPFP/Sinkhorn projection that normalizes mass and drives the marginals to uniformity. This preserves the tractable vine-likelihood structure and the usual copula interpretation while replacing repeated per-edge optimization with GPU inference. Across synthetic and real-data benchmarks, VDC delivers strong bivariate density accuracy, competitive MI/TC estimation, and faster high-dimensional vine fitting. These gains make explicit information estimation and dependence decomposition feasible when repeated vine fitting would otherwise be costly, while conditional downstream tasks remain a limitation.
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