提出可学习有向无环超图的新框架，捕捉多父节点联合影响。
A Framework for Directed Acyclic Hypergraph Learning
- 用乘积交互项的广义线性模型建模超边关系
- 通过张量幂零性约束保证超图无环结构
- 适合需要多变量协同因果推断的研究者
针对现有连续优化方法仅能建模成对因果关系的局限，本文提出从观测数据中学习有向无环超图（DAHGs）的框架。该方法基于三个核心组件：(i) 包含乘积交互项的广义线性结构方程模型（SEM），其非零权重与有向超边一一对应；(ii) 基于加权邻接张量的表示，利用张量t-积定义的幂零性刻画无环性；(iii) 通过t-积的傅里叶分解，将张量幂零性转化为逐切片矩阵幂零性，进而导出可微分的无环性约束，支持使用增广拉格朗日法进行最小二乘学习。
原文摘要 · Abstract (English)
Continuous optimization methods for learning Directed Acyclic Graphs (DAGs) operate on weighted adjacency matrices and are therefore limited to pairwise causal relationships. We propose a framework for learning Directed Acyclic Hypergraphs (DAHGs) from observational data, capturing joint parental influences that pairwise models cannot represent. Our approach rests on three components: (i) a generalized linear structural equation model (SEM) with multiplicative interaction terms whose non-zero weights correspond one-to-one with directed hyperedges; (ii) a weighted adjacency tensor representation whose acyclicity is characterized via nilpotency under the tensor t-product; and (iii) a differentiable acyclicity constraint derived through the Fourier decomposition of the t-product, which reduces tensor nilpotency to slice-wise matrix nilpotency and enables least-squares learning via the augmented Lagrangian method.
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