# Archimedean Copula Inference via Taylor-Mode AD

arXiv: https://arxiv.org/abs/2605.23134 · HTML: https://mlsanity.com/paper/2605.23134/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 44 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 10 of 10)

- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Discrete Copula Diffusion](https://mlsanity.com/paper/2410.01949/) (2024)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Copula-Based Deep Survival Models for Dependent Censoring](https://mlsanity.com/paper/2306.11912/) (2023)
- [You Only Linearize Once: Tangents Transpose to Gradients](https://mlsanity.com/paper/2204.10923/) (2022)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [HACSurv: A Hierarchical Copula-Based Approach for Survival Analysis with Dependent Competing Risks](https://mlsanity.com/paper/2410.15180/) (2024)
- [Automatic Functional Differentiation in JAX](https://mlsanity.com/paper/2311.18727/) (2023)
- [Analysis of multivariate event times under informative censoring using vine copula](https://mlsanity.com/paper/2502.20608/) (2025)

## Abstract (arXiv)

No existing nested Archimedean copula tool handles all three of (a) arbitrary per-variable (right-)censoring in survival analysis, (b) arbitrary nesting trees, and (c) exact parameter gradients. Existing implementations handle only bivariate problems, low dimensional (i.e., d ≤ 10) cases, two layers of nesting, or only hand-derived copula nestings. We present textscacopula, a JAX-native framework that, given any Archimedean generator -- classical or neural -- evaluates exact nested-copula likelihoods and parameter gradients under arbitrary censoring masks in polynomial time. The mechanism is polynomial powering of Taylor-mode automatic differentiation output, which replaces per-family hand-derived partial Bell polynomial tables with a single differentiable computation that any user-defined generator can drive. We conduct extensive simulations to verify the correctness of textscacopula. We then demonstrate (a) per-variable censoring on 85,229 MIMIC-IV ICU admissions in high dimensions with d=53, fit by both classical Archimedean families and nested neural Archimedean copulas; (b) an 11-sector hierarchical model on S&P~500 daily returns at d=98; (c) family-agnostic censored MLE across ten families, five of them with no prior implementation, on a retinopathy study; and (d) a ~650× per-density speedup over R's textttnacLL at d=35, scaling quadratically to d=8,000.