# Deep Archimedean Copulas

arXiv: https://arxiv.org/abs/2012.03137 · HTML: https://mlsanity.com/paper/2012.03137/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2020.

## Built on by (most cited first, 24 of 24)

- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Copula Density Neural Estimation](https://mlsanity.com/paper/2211.15353/) (2022)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence](https://mlsanity.com/paper/2205.01224/) (2022)
- [Deep Copula-Based Survival Analysis for Dependent Censoring with Identifiability Guarantees](https://mlsanity.com/paper/2312.15566/) (2023)
- [Marginal Causal Flows for Validation and Inference](https://mlsanity.com/paper/2411.01295/) (2024)
- [Neural Copula: A unified framework for estimating generic high-dimensional Copula functions](https://mlsanity.com/paper/2205.15031/) (2022)
- [HACSurv: A Hierarchical Copula-Based Approach for Survival Analysis with Dependent Competing Risks](https://mlsanity.com/paper/2410.15180/) (2024)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates](https://mlsanity.com/paper/2206.06462/) (2022)
- [ρ-GNF: A Copula-based Sensitivity Analysis to Unobserved Confounding Using Normalizing Flows](https://mlsanity.com/paper/2209.07111/) (2022)
- [Probabilistic Circuits for Cumulative Distribution Functions](https://mlsanity.com/paper/2408.04229/) (2024)
- [IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulas](https://mlsanity.com/paper/2505.22518/) (2025)
- [Deep Copula Classifier: Theory, Consistency, and Empirical Evaluation](https://mlsanity.com/paper/2505.22997/) (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)
- [2-Cats: 2D Copula Approximating Transforms](https://mlsanity.com/paper/2309.16391/) (2023)
- [A Generative Approach to Quasi-Random Sampling from Copulas via Space-Filling Designs](https://mlsanity.com/paper/2403.05281/) (2024)
- [CoLSE: A Lightweight and Robust Hybrid Learned Model for Single-Table Cardinality Estimation using Joint CDF](https://mlsanity.com/paper/2512.12624/) (2025)
- [Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions](https://mlsanity.com/paper/2605.03061/) (2026)
- [Archimedean Copula Inference via Taylor-Mode AD](https://mlsanity.com/paper/2605.23134/) (2026)
- [Gaussian Mixture Copula Processes for Irregular Time Series](https://mlsanity.com/paper/2605.23632/) (2026)

## Abstract (arXiv)

A central problem in machine learning and statistics is to model joint densities of random variables from data. Copulas are joint cumulative distribution functions with uniform marginal distributions and are used to capture interdependencies in isolation from marginals. Copulas are widely used within statistics, but have not gained traction in the context of modern deep learning. In this paper, we introduce ACNet, a novel differentiable neural network architecture that enforces structural properties and enables one to learn an important class of copulas--Archimedean Copulas. Unlike Generative Adversarial Networks, Variational Autoencoders, or Normalizing Flow methods, which learn either densities or the generative process directly, ACNet learns a generator of the copula, which implicitly defines the cumulative distribution function of a joint distribution. We give a probabilistic interpretation of the network parameters of ACNet and use this to derive a simple but efficient sampling algorithm for the learned copula. Our experiments show that ACNet is able to both approximate common Archimedean Copulas and generate new copulas which may provide better fits to data.