Tensor Network Moral Graph Recovery of Discrete Probability Distributions

2026-09-08

AI Summary

本文提出一种使用全连接张量网络从离散变量的概率分布中恢复因果DAG的道德图的方法，通过核范数正则化键修正来实现。

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 $C_{ij} = U_{ij}V_{ij}^\top$, 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 $\varepsilon = 0$ has effective graph exactly equal to the moral graph. For the approximate regime ($\varepsilon > 0$), 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.

Problem

• moral graph
• causal DAG
• discrete probability distribution

Innovation

• Fully Connected Tensor Networks (FCTNs)
• Nuclear-norm-regularized bond corrections
• Moral graph recovery
• Variational Frobenius norm penalty