Amortized Vine Copulas for High-Dimensional Density and Information Estimation

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.