# Inference and Sampling for Archimax Copulas

arXiv: https://arxiv.org/abs/2205.14025 · HTML: https://mlsanity.com/paper/2205.14025/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 121 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 30 of 31)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Perfect density models cannot guarantee anomaly detection](https://mlsanity.com/paper/2012.03808/) (2020)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Autoregressive Quantile Networks for Generative Modeling](https://mlsanity.com/paper/1806.05575/) (2018)
- [ExGAN: Adversarial Generation of Extreme Samples](https://mlsanity.com/paper/2009.08454/) (2020)
- [Neural Likelihoods via Cumulative Distribution Functions](https://mlsanity.com/paper/1811.00974/) (2018)
- [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)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Multi-Agent Imitation Learning with Copulas](https://mlsanity.com/paper/2107.04750/) (2021)
- [Variational Gaussian Copula Inference](https://mlsanity.com/paper/1506.05860/) (2015)
- [Matrix Completion with Quantified Uncertainty through Low Rank Gaussian Copula](https://mlsanity.com/paper/2006.10829/) (2020)
- [CopulaGNN: Towards Integrating Representational and Correlational Roles of Graphs in Graph Neural Networks](https://mlsanity.com/paper/2010.02089/) (2020)
- [Learning Sparse Latent Representations with the Deep Copula Information Bottleneck](https://mlsanity.com/paper/1804.06216/) (2018)
- [Semi-Supervised Domain Adaptation with Non-Parametric Copulas](https://mlsanity.com/paper/1301.0142/) (2013)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [Robust Correction of Sampling Bias Using Cumulative Distribution Functions](https://mlsanity.com/paper/2010.12687/) (2020)
- [MIND: Inductive Mutual Information Estimation, A Convex Maximum-Entropy Copula Approach](https://mlsanity.com/paper/2102.13182/) (2021)
- [Copula-Based Normalizing Flows](https://mlsanity.com/paper/2107.07352/) (2021)
- [Modeling Extremes with d-max-decreasing Neural Networks](https://mlsanity.com/paper/2102.09042/) (2021)
- [Copula-like Variational Inference](https://mlsanity.com/paper/1904.07153/) (2019)
- [Gaussian Process Vine Copulas for Multivariate Dependence](https://mlsanity.com/paper/1302.3979/) (2013)
- [Gaussian Process Conditional Copulas with Applications to Financial Time Series](https://mlsanity.com/paper/1307.0373/) (2013)
- [On structure, family and parameter estimation of hierarchical Archimedean copulas](https://mlsanity.com/paper/1611.09225/) (2016)

## Built on by (most cited first, 5 of 5)

- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Retrospective Uncertainties for Deep Models using Vine Copulas](https://mlsanity.com/paper/2302.12606/) (2023)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulas](https://mlsanity.com/paper/2505.22518/) (2025)
- [A Generative Approach to Quasi-Random Sampling from Copulas via Space-Filling Designs](https://mlsanity.com/paper/2403.05281/) (2024)

## Abstract (arXiv)

Understanding multivariate dependencies in both the bulk and the tails of a distribution is an important problem for many applications, such as ensuring algorithms are robust to observations that are infrequent but have devastating effects. Archimax copulas are a family of distributions endowed with a precise representation that allows simultaneous modeling of the bulk and the tails of a distribution. Rather than separating the two as is typically done in practice, incorporating additional information from the bulk may improve inference of the tails, where observations are limited. Building on the stochastic representation of Archimax copulas, we develop a non-parametric inference method and sampling algorithm. Our proposed methods, to the best of our knowledge, are the first that allow for highly flexible and scalable inference and sampling algorithms, enabling the increased use of Archimax copulas in practical settings. We experimentally compare to state-of-the-art density modeling techniques, and the results suggest that the proposed method effectively extrapolates to the tails while scaling to higher dimensional data. Our findings suggest that the proposed algorithms can be used in a variety of applications where understanding the interplay between the bulk and the tails of a distribution is necessary, such as healthcare and safety.