Amortized Vine Copulas for High-Dimensional Density and Information Estimation
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| Format: | Preprint |
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2026
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| _version_ | 1866910195083378688 |
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| author | Safaai, Houman |
| author_facet | Safaai, Houman |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20568 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Amortized Vine Copulas for High-Dimensional Density and Information Estimation Safaai, Houman Machine Learning Information Theory Methodology 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. |
| title | Amortized Vine Copulas for High-Dimensional Density and Information Estimation |
| topic | Machine Learning Information Theory Methodology |
| url | https://arxiv.org/abs/2604.20568 |