Amortized Vine Copulas for High-Dimensional Density and Information Estimation

2026-04-22

AI Summary

Modeling high-dimensional dependencies often struggles to balance tractable likelihood evaluation with structural interpretability. This work proposes the Vine Denoising Copula (VDC), which introduces amortized inference into the vine copula framework for the first time. By employing a single shared bivariate denoising model across all vine edges, VDC leverages pseudo-observation inputs combined with IPFP or Sinkhorn projections to ensure valid density estimation, while GPU acceleration enables efficient inference. The method preserves the interpretability inherent in vine copulas and substantially improves high-dimensional fitting efficiency. Empirical evaluations on both synthetic and real-world datasets demonstrate highly accurate bivariate density estimates and competitive performance in mutual information and total correlation estimation.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models
• Computer Vision: Diffusion Models for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• high-dimensional density estimation
• information estimation
• vine copulas
• dependency modeling
• tractable likelihood

Innovation

• amortized inference
• vine copulas
• denoising model
• Sinkhorn projection
• high-dimensional density estimation