Semiparametric Bayesian structure learning of nonparanormal directed acyclic graphs with local--global shrinkage
Abstract
Bayesian structure learning of directed acyclic graphs (DAGs) is central to high-dimensional causal discovery, yet existing methods mostly assume multivariate Gaussian data, which is routinely violated by measurements displaying heavy tails, skewness, or bounded support. We address this by introducing NPN-DAG-HS, a fully Bayesian semiparametric DAG model coupling the nonparanormal family with horseshoe shrinkage on Cholesky off-diagonals via an extended-rank likelihood. This handles arbitrary unknown monotone marginal transformations without estimating them, preserving exact-zero shrinkage and conditionally conjugate posteriors for practical inference in large dimensions. Our method uses a partially collapsed Metropolis-within-Gibbs sampler that augments rank-likelihood Gaussian copies and alternates score-based DAG moves with horseshoe Gibbs updates. Theoretically, in the high-dimensional regime (p → ∞ with log p / n → 0), we establish posterior contraction at the rate √((s0+p)log p/n), strong skeleton selection consistency, and a parametric Bernstein-von Mises theorem for smooth total causal-effect functionals, yielding asymptotic frequentist calibration of credible intervals. Simulations confirm our method outperforms Gaussian baselines and standard frequentist learners. Applied to an acute myeloid leukaemia dataset, it recovers a sparse, interpretable network, pruning unsupported edges declared by Gaussian analyses and illustrating the value of our semiparametric relaxation.
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BibTeX
@misc{nazari2026semiparametric,
title = {{Semiparametric Bayesian structure learning of nonparanormal directed acyclic graphs with local--global shrinkage}},
author = {Samaneh Nazari and Mohammad Arashi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13007},
eprint = {2609.13007},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13007},
}
RIS
TY - UNPB
TI - Semiparametric Bayesian structure learning of nonparanormal directed acyclic graphs with local--global shrinkage
AU - Samaneh Nazari
AU - Mohammad Arashi
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.13007
UR - https://arxiv.org/abs/2609.13007
AB - Bayesian structure learning of directed acyclic graphs (DAGs) is central to high-dimensional causal discovery, yet existing methods mostly assume multivariate Gaussian data, which is routinely violated by measurements displaying heavy tails, skewness, or bounded support. We address this by introducing NPN-DAG-HS, a fully Bayesian semiparametric DAG model coupling the nonparanormal family with horseshoe shrinkage on Cholesky off-diagonals via an extended-rank likelihood. This handles arbitrary unknown monotone marginal transformations without estimating them, preserving exact-zero shrinkage and conditionally conjugate posteriors for practical inference in large dimensions. Our method uses a partially collapsed Metropolis-within-Gibbs sampler that augments rank-likelihood Gaussian copies and alternates score-based DAG moves with horseshoe Gibbs updates. Theoretically, in the high-dimensional regime (p → ∞ with log p / n → 0), we establish posterior contraction at the rate √((s_0+p)log p/n), strong skeleton selection consistency, and a parametric Bernstein-von Mises theorem for smooth total causal-effect functionals, yielding asymptotic frequentist calibration of credible intervals. Simulations confirm our method outperforms Gaussian baselines and standard frequentist learners. Applied to an acute myeloid leukaemia dataset, it recovers a sparse, interpretable network, pruning unsupported edges declared by Gaussian analyses and illustrating the value of our semiparametric relaxation.
ER -