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 \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 ∼650× per-density speedup over R's \texttt{nacLL} at d=35, scaling quadratically to d=8,000.
Modeling high-dimensional dependencies while keeping likelihoods tractable remains challenging. Classical vine-copula pipelines are interpretable but can be expensive, while many neural estimators are flexible but less structured. In this work, we propose Vine Denoising Copula (VDC), an amortized vine-copula pipeline for continuous-data, simplified-vine dependence modeling. VDC trains a single bivariate denoising model and reuses it across all vine edges. For each edge, given pseudo-observations, the model predicts a piecewise-constant density grid. We then apply an IPFP/Sinkhorn projection that normalizes mass and drives the marginals to uniformity. This preserves the tractable vine-likelihood structure and the usual copula interpretation while replacing repeated per-edge optimization with GPU inference. Across synthetic and real-data benchmarks, VDC delivers strong bivariate density accuracy, competitive MI/TC estimation, and faster high-dimensional vine fitting. These gains make explicit information estimation and dependence decomposition feasible when repeated vine fitting would otherwise be costly, while conditional downstream tasks remain a limitation.
Dependent censoring occurs when the event time and censoring time are not conditionally independent given the observed covariates. This complicates survival model evaluation because widely used metrics, such as the Brier score, typically handle right-censoring using inverse probability of censoring weighting (IPCW). Unfortunately, IPCW is valid only when the estimated censoring distribution is independent of the event time. We propose a dependent Brier score based on an Archimedean copula and the Copula-Graphic estimator, and establish consistency and asymptotic normality of its margin-time estimator. To evaluate the metric, we introduce a semi-synthetic framework that creates realistic dependent censoring while preserving the original covariate structure and known event times. Across 12 datasets, the proposed metric reduces estimation error by 12-16% on average relative to IPCW. Source code is available at https://github.com/thecml/DependentEVAL.
Christian Marius Lillelund, Shi-ang Qi, Russell Greiner
Deep generative models offer powerful tools for multivariate data analysis, but their black-box architectures are often unidentified and difficult to interpret. We introduce the Deep Discrete Encoder (DDE) Copula, an identifiable and interpretable generative model for multivariate data with arbitrary marginal distributions. The model places a hierarchical directed network of binary latent variables inside a copula framework, enabling flexible dependence modeling for mixed discrete and continuous data. Estimation is based on rank likelihoods, which decouple marginal modeling from posterior inference on the DDE parameters and avoid specifying the marginal distributions. We establish conditions for identification of the DDE copula parameters, ensuring that layer-specific parameters provide meaningful summaries of multivariate dependence. We also prove quotient-space posterior consistency for continuous margins under the exact rank likelihood and treat the extended rank likelihood for tied or mixed margins as a generalized likelihood, with concentration under an additional contrast condition. For computation, we propose a stochastic expectation-maximization algorithm for \emph{maximum a posteriori} estimation, together with initialization strategies that improve convergence. To learn network dimension adaptively, we extend Bayesian rank-selection priors to infer layer-specific widths. Simulations show strong finite-sample performance, and a personality-survey analysis reveals interpretable hierarchical latent structure in complex multivariate data.