# IGNIS: A Robust Neural Network Framework for Constrained Parameter Estimation in Archimedean Copulas

arXiv: https://arxiv.org/abs/2505.22518 · HTML: https://mlsanity.com/paper/2505.22518/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 25 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 5 of 5)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)

## Built on by (most cited first, 1 of 1)

- [Copula Based Fusion of Clinical and Genomic Machine Learning Risk Scores for Breast Cancer Risk Stratification](https://mlsanity.com/paper/2511.17605/) (2025)

## Abstract (arXiv)

Classical estimators, the cornerstones of statistical inference, face insurmountable challenges when applied to important emerging classes of Archimedean copulas. These models exhibit pathological properties, including numerically unstable densities, a restrictive lower bound on Kendall's tau, and vanishingly small likelihood gradients, making MLE brittle and limiting MoM's applicability to datasets with sufficiently strong dependence (i.e., only when the empirical Kendall's τ exceeds the family's lower bound ≈ 0.545). We introduce IGNIS, a unified neural estimation framework that sidesteps these barriers by learning a direct, robust mapping from data-driven dependency measures to the underlying copula parameter θ. IGNIS utilizes a multi-input architecture and a theory-guided output layer (softplus(z) + 1) to automatically enforce the domain constraint hatθ ≥ 1. Trained and validated on four families (Gumbel, Joe, and the numerically challenging A1/A2), IGNIS delivers accurate and stable estimates for real-world financial and health datasets, demonstrating its necessity for reliable inference in modern, complex dependence models where traditional methods fail. To our knowledge, IGNIS is the first standalone, general-purpose neural estimator for Archimedean copulas (not a generative model or likelihood optimizer), delivering direct, constraint-aware hatθ and readily extensible to additional families via retraining or minor output-layer adaptations.