Archimedean Copula Inference via Taylor-Mode AD

No existing nested Archimedean copula tool handles all three of (a) arbitrary per-variable (right-)censoring in survival analysis, (b) arbitrary nesting trees, and © exact parameter gradients. Existing implementations handle only bivariate problems, low dimensional (i.e., $d\le 10$) cases, two layers of nesting, or only hand-derived copula nestings. We present $\text{textsc}acopula$, 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 $\text{textsc}acopula$. We then demonstrate (a) per-variable censoring on $\mathrm{85,229}$ 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 $d=98$; © 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 $\mathtt{\text{nacLL}}$ at $d=35$, scaling quadratically to $d=\mathrm{8,000}$.