Amortized Vine Copulas for High-Dimensional Density and Information Estimation

arXiv cs.LG / 4/23/2026

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Key Points

The paper introduces Vine Denoising Copula (VDC), an amortized vine-copula approach designed to model high-dimensional dependencies with tractable likelihoods.
VDC trains a single bivariate denoising model and reuses it across all vine edges, avoiding expensive per-edge optimization common in classical vine-copula pipelines.
For each vine edge, the model predicts a density grid from pseudo-observations, and an IPFP/Sinkhorn projection enforces non-negativity, unit mass, and uniform marginals while preserving exact vine likelihood and copula interpretability.
Experiments on synthetic and real data show strong bivariate density accuracy, competitive mutual-information and total-correlation estimation, and significant speedups for high-dimensional vine fitting.
The authors conclude that VDC makes explicit information estimation and dependence decomposition feasible at larger scales, though downstream conditional inference results are mixed.

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 that trains a single bivariate denoising model and reuses it across all vine edges. For each edge, given pseudo-observations, the model predicts a density grid. We then apply an IPFP/Sinkhorn projection that enforces non-negativity, unit mass, and uniform marginals. This keeps the exact vine likelihood and preserves 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 substantial speedups for high-dimensional vine fitting. In practice, these gains make explicit information estimation and dependence decomposition feasible at scales where repeated vine fitting would otherwise be costly, although conditional downstream inference remains mixed.