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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.23134 |
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| _version_ | 1866917522916245504 |
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| author | Yang, Cambridge Li, Dongdong |
| author_facet | Yang, Cambridge Li, Dongdong |
| contents | 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., $d \leq 10$) cases, two layers of nesting, or only hand-derived copula nestings. We present \textsc{acopula}, 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 \textsc{acopula}. 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 ${\sim}650\times$ per-density speedup over R's \texttt{nacLL} at $d{=}35$, scaling quadratically to $d{=}8{,}000$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23134 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Archimedean Copula Inference via Taylor-Mode AD Yang, Cambridge Li, Dongdong Machine Learning 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., $d \leq 10$) cases, two layers of nesting, or only hand-derived copula nestings. We present \textsc{acopula}, 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 \textsc{acopula}. 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 ${\sim}650\times$ per-density speedup over R's \texttt{nacLL} at $d{=}35$, scaling quadratically to $d{=}8{,}000$. |
| title | Archimedean Copula Inference via Taylor-Mode AD |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.23134 |