将藤蔓耦合模型转为可微计算图,提升机器学习中的不确定性建模效率。
Vine Copulas as Differentiable Computational Graphs
- 把藤蔓耦合结构抽象成有向无环图,支持自动微分和梯度传播。
- 在深度学习中用藤蔓耦合量化不确定性,性能优于MC-dropout等方法。
- 适用于需要精准概率估计的现代机器学习任务,如自编码器与贝叶斯推理。
藤蔓耦合模型是复杂的多变量分布建模工具,正日益应用于机器学习。为促进其融入现代机器学习流程,我们提出藤蔓计算图,一种抽象多层藤蔓结构及其计算过程的有向无环图。在此基础上,我们设计了新的条件采样算法、高效的采样顺序调度策略,以及针对定制化条件变量的藤蔓结构构建方法。我们在PyTorch基础上实现torchvinecopulib,一个支持GPU加速的Python库,显著提升了拟合、采样和密度评估的可扩展性。实验表明,通过藤蔓结构传递梯度可改进藤蔓耦合自编码器;在不确定性量化方面,该方法在锐度、校准性和运行时间上均优于MC-dropout、深度集成和贝叶斯神经网络。本工作将经典依赖建模与现代深度学习工具链结合,推动先进耦合方法在现代机器学习流水线中的应用。
原文摘要 · Abstract (English)
Vine copulas are sophisticated models for multivariate distributions and are increasingly used in machine learning. To facilitate their integration into modern ML pipelines, we introduce the vine computational graph, a DAG that abstracts the multilevel vine structure and associated computations. On this foundation, we devise new algorithms for conditional sampling, efficient sampling-order scheduling, and constructing vine structures for customized conditioning variables. We implement these ideas in torchvinecopulib, a GPU-accelerated Python library built upon PyTorch, delivering improved scalability for fitting, sampling, and density evaluation. Our experiments illustrate how gradient flowing through the vine can improve Vine Copula Autoencoders and that incorporating vines for uncertainty quantification in deep learning can outperform MC-dropout, deep ensembles, and Bayesian Neural Networks in sharpness, calibration, and runtime. By recasting vine copula models as computational graphs, our work connects classical dependence modeling with modern deep-learning toolchains and facilitates the integration of state-of-the-art copula methods in modern machine learning pipelines.
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