用扩散与流模型构建新型拷贝函数，更灵活地捕捉高维依赖关系。
Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies
- 通过渐进遗忘变量间依赖的扩散/流过程，构造可验证的有效拷贝函数。
- 在科学数据与图像上优于现有方法，能准确建模复杂高维依赖。
- 适合需要精确建模多变量关系的研究者，如金融、生物统计等场景。
拷贝函数是建模多变量依赖关系的基础工具，广泛应用于多个领域。然而，现有模型在处理多模态和高维依赖时受限于严格假设且扩展性差。本文基于扩散与流的原理提出建模拷贝函数的新方法：设计两种逐步遗忘变量间依赖但保持边缘分布不变的过程，理论上保证任意时刻均为有效拷贝函数。通过学习从这些过程中恢复被遗忘的依赖关系，可理论重构真实拷贝函数。首个实例聚焦直接密度估计，第二个侧重高效采样。实验证明，该方法在科学数据集与图像上的高维复杂依赖建模中显著优于当前最优拷贝函数方法。本工作提升了拷贝函数的表达能力，推动其在更大规模与更挑战性任务中的应用。
原文摘要 · Abstract (English)
Copulas are a fundamental tool for modelling multivariate dependencies in data, forming the method of choice in diverse fields and applications. However, the adoption of existing models for multimodal and high-dimensional dependencies is hindered by restrictive assumptions and poor scaling. In this work, we present methods for modelling copulas based on the principles of diffusions and flows. We design two processes that progressively forget inter-variable dependencies while leaving dimension-wise distributions unaffected, provably defining valid copulas at all times. We show how to obtain copula models by learning to remember the forgotten dependencies from each process, theoretically recovering the true copula at optimality. The first instantiation of our framework focuses on direct density estimation, while the second specialises in expedient sampling. Empirically, we demonstrate the superior performance of our proposed methods over state-of-the-art copula approaches in modelling complex and high-dimensional dependencies from scientific datasets and images. Our work enhances the representational power of copula models, empowering applications and paving the way for their adoption on larger scales and more challenging domains.
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