Archimedean Copula Inference via Taylor-Mode AD

arXiv:2605.23134v1 Announce Type: new Abstract: 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 extsc{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 extsc{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}650imes per-density speedup over R's exttt{nacLL} at d{=}35, scaling quadratically to d{=}8{,}000.

Source: arXiv cs.LG | 2026-05-25