Vine Copulas as Differentiable Computational Graphs

TL;DR

This paper introduces a differentiable computational graph framework for vine copulas, enabling their integration into machine learning pipelines with improved scalability, sampling, and uncertainty quantification capabilities.

Contribution

We present the vine computational graph, a novel DAG-based abstraction that facilitates efficient algorithms and GPU-accelerated implementation for vine copulas in deep learning.

Findings

Gradient flow through vines improves autoencoder performance

Vine-based uncertainty quantification outperforms MC-dropout and ensembles

New algorithms enable scalable sampling and structure construction

Abstract

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.