Tensor Network Moral Graph Recovery of Discrete Probability Distributions
Abstract
We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction Cij = UijVij⊤, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, \textbf{every} optimal FCTN with zero reconstruction error ε = 0 has effective graph exactly equal to the moral graph. For the approximate regime (ε > 0), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter β. The effective graph is read directly from the optimized bond matrices.
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BibTeX
@misc{olivas2026tensor,
title = {{Tensor Network Moral Graph Recovery of Discrete Probability Distributions}},
author = {Á. Troyano Olivas and Chi-Hang Fred Fung and Hans H. Brunner and Momtchil Peev and Vicente Martin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09258},
eprint = {2609.09258},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09258},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tensor Network Moral Graph Recovery of Discrete Probability Distributions
AU - Á. Troyano Olivas
AU - Chi-Hang Fred Fung
AU - Hans H. Brunner
AU - Momtchil Peev
AU - Vicente Martin
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09258
UR - https://arxiv.org/abs/2609.09258
AB - We present a method for recovering the moral graph of a causal DAG from a probability distribution over discrete variables, using fully connected tensor networks (FCTNs) with nuclear-norm-regularized bond corrections. Each bond matrix is parameterized as a baseline all-ones matrix plus a low-rank correction C_ij = U_ijV_ij^⊤, and the nuclear norm of the correction implemented via the variational Frobenius norm penalty on the factors drives unnecessary bonds to zero. We prove that under faithfulness, positivity, and a no-implicit-rerouting assumption on the local tensor architecture, \textbf{every} optimal FCTN with zero reconstruction error ε = 0 has effective graph exactly equal to the moral graph. For the approximate regime (ε > 0), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter β. The effective graph is read directly from the optimized bond matrices.
ER -