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acopula

Archimedean copula inference via Taylor-mode automatic differentiation in JAX.

acopula fits nested Archimedean copulas end-to-end with jax.grad — including high-dimensional models, per-dimension censoring, and Bell-polynomial densities derived automatically from the user-supplied generator. The high-order derivatives that previously bottlenecked nested-Archimedean likelihoods (limiting prior tools to roughly d=10) are computed in a single forward pass via Taylor-mode AD, scaling polynomially in the dimension.

Install

pip install git+https://github.com/thisiscam/acopula

acopula depends on a patched oryx build (pulled from git during install) because stock oryx is incompatible with jax 0.8. For development, clone and use uv:

git clone https://github.com/thisiscam/acopula
cd acopula
uv sync                 # add --extra examples for the plotting examples
uv run python examples/01_quickstart.py

A PyPI pip install acopula is not available yet: the git-pinned oryx dependency can't be uploaded to PyPI, so it is gated on an upstream oryx release compatible with jax 0.8.

acopula pins jax>=0.8,<0.9 because it relies on JAX-internal APIs in the jet-array backend.

Features

  • Nested Archimedean copulas of arbitrary depth and arity.
  • Per-dimension censoring — each leaf can be independently right-censored per observation; one XLA program handles all masks.
  • Density via Bell polynomials, computed from a Taylor expansion of the generator rather than nested first-order AD.
  • Symbolic generator inversion via oryx, with bisection + IFT fallback.
  • Sampling via the Marshall-Olkin algorithm and the Rosenblatt transform.
  • Validity diagnostic — per-edge d_c-monotonicity check for cross-family nesting.

Where to go next

  • Quickstart — a working model in ~20 lines.
  • Examples — runnable notebooks: MLE fitting, censored survival, sampling & plots, a neural (ACNet) generator.
  • API reference — the full public surface.

Citation

@misc{yang2026copulaad,
  title={Archimedean Copula Inference via Taylor-Mode AD},
  author={Yang, Cambridge and Li, Dongdong},
  year={2026},
  note={arXiv preprint},
}