# Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas

arXiv: https://arxiv.org/abs/1503.03305 · HTML: https://mlsanity.com/paper/1503.03305/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2015.

## Built on by (most cited first, 18 of 18)

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- [Neural Conditional Probability for Uncertainty Quantification](https://mlsanity.com/paper/2407.01171/) (2024)
- [Copula Density Neural Estimation](https://mlsanity.com/paper/2211.15353/) (2022)
- [RoCourseNet: Distributionally Robust Training of a Prediction Aware Recourse Model](https://mlsanity.com/paper/2206.00700/) (2022)
- [Explaining predictive models using Shapley values and non-parametric vine copulas](https://mlsanity.com/paper/2102.06416/) (2021)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [A General Approach for Determining Applicability Domain of Machine Learning Models](https://mlsanity.com/paper/2406.05143/) (2024)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [ROME: Robust Multi-Modal Density Estimator](https://mlsanity.com/paper/2401.10566/) (2024)
- [Edge Case Detection in Automated Driving: Methods, Challenges, and Future Directions](https://mlsanity.com/paper/2410.08491/) (2024)
- [Graphical Transformation Models](https://mlsanity.com/paper/2503.17845/) (2025)
- [MCD: Marginal Contrastive Discrimination for conditional density estimation](https://mlsanity.com/paper/2206.01592/) (2022)
- [Hybrid Bernstein Normalizing Flows for Flexible Multivariate Density Regression with Interpretable Marginals](https://mlsanity.com/paper/2505.14164/) (2025)
- [Binned semiparametric Bayesian networks for efficient kernel density estimation](https://mlsanity.com/paper/2506.21997/) (2025)
- [Knowledge Cascade: Reverse Knowledge Distillation on Nonparametric Multivariate Functional Estimation](https://mlsanity.com/paper/2606.25927/) (2026)
- [Breaking the Curse with BAND: Nonparametric Distribution Estimation in High Dimensions](https://mlsanity.com/paper/2607.26955/) (2026)
- [Semiparametric Inference for Conditional Shapley Feature Importance](https://mlsanity.com/paper/2609.10313/) (2026)

## Abstract (arXiv)

Practical applications of nonparametric density estimators in more than three dimensions suffer a great deal from the well-known curse of dimensionality: convergence slows down as dimension increases. We show that one can evade the curse of dimensionality by assuming a simplified vine copula model for the dependence between variables. We formulate a general nonparametric estimator for such a model and show under high-level assumptions that the speed of convergence is independent of dimension. We further discuss a particular implementation for which we validate the high-level assumptions and establish its asymptotic normality. Simulation experiments illustrate a large gain in finite sample performance when the simplifying assumption is at least approximately true. But even when it is severely violated, the vine copula based approach proves advantageous as soon as more than a few variables are involved. Lastly, we give an application of the estimator to a classification problem from astrophysics.