Amortized Vine Copulas for High-Dimensional Density and Information Estimation

TL;DR

This paper introduces Vine Denoising Copula (VDC), an efficient neural approach for high-dimensional dependence modeling that maintains interpretability and improves computational speed over traditional methods.

Contribution

VDC trains a single denoising model reused across vine edges, enabling fast, accurate high-dimensional density and information estimation with a structured, neural-based pipeline.

Findings

VDC achieves high bivariate density accuracy on benchmarks.

It provides competitive mutual information and tail dependence estimates.

VDC offers faster high-dimensional vine fitting compared to traditional methods.

Abstract

Modeling high-dimensional dependencies while keeping likelihoods tractable remains challenging. Classical vine-copula pipelines are interpretable but can be expensive, while many neural estimators are flexible but less structured. In this work, we propose Vine Denoising Copula (VDC), an amortized vine-copula pipeline for continuous-data, simplified-vine dependence modeling. VDC trains a single bivariate denoising model and reuses it across all vine edges. For each edge, given pseudo-observations, the model predicts a piecewise-constant density grid. We then apply an IPFP/Sinkhorn projection that normalizes mass and drives the marginals to uniformity. This preserves the tractable vine-likelihood structure and the usual copula interpretation while replacing repeated per-edge optimization with GPU inference. Across synthetic and real-data benchmarks, VDC delivers strong bivariate density accuracy, competitive MI/TC estimation, and faster high-dimensional vine fitting. These gains make explicit information estimation and dependence decomposition feasible when repeated vine fitting would otherwise be costly, while conditional downstream tasks remain a limitation.