# Your copula is a classifier in disguise: classification-based copula density estimation

arXiv: https://arxiv.org/abs/2411.03014 · HTML: https://mlsanity.com/paper/2411.03014/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 77 references that are in the map.
- First posted on arXiv 5 Nov 2024.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning in Implicit Generative Models](https://mlsanity.com/paper/1610.03483/) (2016)
- [Telescoping Density-Ratio Estimation](https://mlsanity.com/paper/2006.12204/) (2020)
- [Density Ratio Estimation via Infinitesimal Classification](https://mlsanity.com/paper/2111.11010/) (2021)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Featurized Density Ratio Estimation](https://mlsanity.com/paper/2107.02212/) (2021)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders](https://mlsanity.com/paper/1906.05423/) (2019)
- [Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas](https://mlsanity.com/paper/1503.03305/) (2015)
- [Adaptive Multi-stage Density Ratio Estimation for Learning Latent Space Energy-based Model](https://mlsanity.com/paper/2209.08739/) (2022)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Estimating the Density Ratio between Distributions with High Discrepancy using Multinomial Logistic Regression](https://mlsanity.com/paper/2305.00869/) (2023)
- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Multi-Agent Imitation Learning with Copulas](https://mlsanity.com/paper/2107.04750/) (2021)
- [Semiparametric conformal prediction](https://mlsanity.com/paper/2411.02114/) (2024)
- [Probit transformation for nonparametric kernel estimation of the copula density](https://mlsanity.com/paper/1404.4414/) (2014)
- [Quasi-random sampling for multivariate distributions via generative neural networks](https://mlsanity.com/paper/1811.00683/) (2018)
- [Semi-Supervised Domain Adaptation with Non-Parametric Copulas](https://mlsanity.com/paper/1301.0142/) (2013)
- [Estimation of copulas via Maximum Mean Discrepancy](https://mlsanity.com/paper/2010.00408/) (2020)
- [MIND: Inductive Mutual Information Estimation, A Convex Maximum-Entropy Copula Approach](https://mlsanity.com/paper/2102.13182/) (2021)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [Probabilistic Rainfall Downscaling: Joint Generalized Neural Models with Censored Spatial Gaussian Copula](https://mlsanity.com/paper/2308.09827/) (2023)

## Built on by (most cited first, 8 of 8)

- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [Neural Mutual Information Estimation with Vector Copulas](https://mlsanity.com/paper/2510.20968/) (2025)
- [A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction](https://mlsanity.com/paper/2601.19175/) (2026)
- [Amortized Vine Copulas for High-Dimensional Density and Information Estimation](https://mlsanity.com/paper/2604.20568/) (2026)
- [Learning density ratios in causal inference using Bregman-Riesz regression](https://mlsanity.com/paper/2510.16127/) (2025)
- [Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions](https://mlsanity.com/paper/2605.03061/) (2026)
- [Probabilistic Multivariate Time Series Forecasting with Diffusion Copulas](https://mlsanity.com/paper/2605.19685/) (2026)
- [K-IPO: Kendall-constrained Importance Preserving Oversampling for Imbalanced Tabular Data](https://mlsanity.com/paper/2607.16478/) (2026)

## Abstract (arXiv)

We propose reinterpreting copula density estimation as a discriminative task. Under this novel estimation scheme, we train a classifier to distinguish samples from the joint density from those of the product of independent marginals, recovering the copula density in the process. We derive equivalences between well-known copula classes and classification problems naturally arising in our interpretation. Furthermore, we show our estimator achieves theoretical guarantees akin to maximum likelihood estimation. By identifying a connection with density ratio estimation, we benefit from the rich literature and models available for such problems. Empirically, we demonstrate the applicability of our approach by estimating copulas of real and high-dimensional datasets, outperforming competing copula estimators in density evaluation as well as sampling.