# Vine Copulas as Differentiable Computational Graphs

arXiv: https://arxiv.org/abs/2506.13318 · HTML: https://mlsanity.com/paper/2506.13318/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 65 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Builds on (most cited first, 18 of 18)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders](https://mlsanity.com/paper/1906.05423/) (2019)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Semiparametric conformal prediction](https://mlsanity.com/paper/2411.02114/) (2024)
- [On boosting the power of Chatterjee's rank correlation](https://mlsanity.com/paper/2108.06828/) (2021)
- [Explaining predictive models using Shapley values and non-parametric vine copulas](https://mlsanity.com/paper/2102.06416/) (2021)
- [Prediction based on conditional distributions of vine copulas](https://mlsanity.com/paper/1807.08429/) (2018)
- [Retrospective Uncertainties for Deep Models using Vine Copulas](https://mlsanity.com/paper/2302.12606/) (2023)
- [From Dependence to Causation](https://mlsanity.com/paper/1607.03300/) (2016)
- [D-vine copula based quantile regression](https://mlsanity.com/paper/1510.04161/) (2015)
- [Nonparametric C- and D-vine based quantile regression](https://mlsanity.com/paper/2102.04873/) (2021)
- [Solving estimating equations with copulas](https://mlsanity.com/paper/1801.10576/) (2018)
- [fastMI: a fast and consistent copula-based estimator of mutual information](https://mlsanity.com/paper/2212.10268/) (2022)
- [Vine copula mixture models and clustering for non-Gaussian data](https://mlsanity.com/paper/2102.03257/) (2021)

## Built on by (most cited first, 2 of 2)

- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)
- [Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions](https://mlsanity.com/paper/2605.03061/) (2026)

## Abstract (arXiv)

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.