# Copula Density Neural Estimation

arXiv: https://arxiv.org/abs/2211.15353 · HTML: https://mlsanity.com/paper/2211.15353/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [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)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Multi-Agent Imitation Learning with Copulas](https://mlsanity.com/paper/2107.04750/) (2021)
- [Neural Copula: A unified framework for estimating generic high-dimensional Copula functions](https://mlsanity.com/paper/2205.15031/) (2022)

## Built on by (most cited first, 13 of 13)

- [MINDE: Mutual Information Neural Diffusion Estimation](https://mlsanity.com/paper/2310.09031/) (2023)
- [Mutual Information Estimation via f-Divergence and Data Derangements](https://mlsanity.com/paper/2305.20025/) (2023)
- [f-Divergence Based Classification: Beyond the Use of Cross-Entropy](https://mlsanity.com/paper/2401.01268/) (2024)
- [Information Theoretic Text-to-Image Alignment](https://mlsanity.com/paper/2405.20759/) (2024)
- [Marginal Causal Flows for Validation and Inference](https://mlsanity.com/paper/2411.01295/) (2024)
- [Neural Mutual Information Estimation with Vector Copulas](https://mlsanity.com/paper/2510.20968/) (2025)
- [Diffusion Secant Alignment for Score-Based Density Ratio Estimation](https://mlsanity.com/paper/2509.04852/) (2025)
- [CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks](https://mlsanity.com/paper/2605.12580/) (2026)
- [INFO-SEDD: Continuous Time Markov Chains as Scalable Information Metrics Estimators](https://mlsanity.com/paper/2502.19183/) (2025)
- [Why Do Unlearnable Examples Work: A Novel Perspective of Mutual Information](https://mlsanity.com/paper/2603.03725/) (2026)
- [Masked Language Modeling Becomes Conditional Density Estimation for Tabular Data Synthesis](https://mlsanity.com/paper/2405.20602/) (2024)
- [Amortized Vine Copulas for High-Dimensional Density and Information Estimation](https://mlsanity.com/paper/2604.20568/) (2026)
- [Capturing Multivariate Dependencies of EV Charging Events: From Parametric Copulas to Neural Density Estimation](https://mlsanity.com/paper/2603.29554/) (2026)

## Abstract (arXiv)

Probability density estimation from observed data constitutes a central task in statistics. In this brief, we focus on the problem of estimating the copula density associated to any observed data, as it fully describes the dependence between random variables. We separate univariate marginal distributions from the joint dependence structure in the data, the copula itself, and we model the latter with a neural network-based method referred to as copula density neural estimation (CODINE). Results show that the novel learning approach is capable of modeling complex distributions and can be applied for mutual information estimation and data generation.