Tensor Network Moral Graph Recovery of Discrete Probability Distributions

arXiv:2609.09258v1 Announce Type: cross 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 C_{ij} = U_{ij}V_{ij}^op, 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, extbf{every} optimal FCTN with zero reconstruction error arepsilon = 0 has effective graph exactly equal to the moral graph. For the approximate regime (arepsilon > 0), we provide explicit recovery bounds using the Fannes-Audenaert continuity of conditional mutual information, and derive a sufficient condition on the regularization parameter eta. The effective graph is read directly from the optimized bond matrices.

Joint Bayesian Parameter and Model Order Estimation for Low-Rank Probability Mass Tensors

Source: arXiv cs.LG | 2026-09-10

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