Vine Copulas as Differentiable Computational Graphs
This work addresses the problem of connecting classical dependence modeling with deep learning toolchains for researchers and practitioners in machine learning, representing a novel method for a known bottleneck rather than an incremental improvement.
The authors tackled the challenge of integrating vine copulas into modern machine learning pipelines by introducing a computational graph representation, which enabled new algorithms for conditional sampling and structure construction, implemented in a GPU-accelerated library. Their experiments showed that this approach improved Vine Copula Autoencoders and outperformed methods like MC-dropout, deep ensembles, and Bayesian Neural Networks in sharpness, calibration, and runtime for uncertainty quantification.
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.