In statistics and machine learning, detecting dependencies in datasets is a
central challenge. We propose a novel neural network model for supervised graph
structure learning, i.e., the process of learning a mapping between
observational data and their underlying dependence structure. The model is
trained with variably shaped and coupled simulated input data and requires only
a single forward pass through the trained network for inference. By leveraging
structural equation models and employing randomly generated multivariate
Chebyshev polynomials for the simulation of training data, our method
demonstrates robust generalizability across both linear and various types of
non-linear dependencies. We introduce a novel bilinear attention mechanism
(BAM) for explicit processing of dependency information, which operates on the
level of covariance matrices of transformed data and respects the geometry of
the manifold of symmetric positive definite matrices. Empirical evaluation
demonstrates the robustness of our method in detecting a wide range of
dependencies, excelling in undirected graph estimation and proving competitive
in completed partially directed acyclic graph estimation through a novel
two-step approach.

统计学和机器学习中，检测数据集中的依赖关系是一个核心挑战。我们提出了一种新颖的神经网络模型，用于监督式图结构学习，即学习观测数据与其底层依赖结构之间的映射关系。通过利用结构方程模型和使用随机生成的多元切比雪夫多项式来模拟训练数据，我们的方法在线性和各种类型的非线性依赖关系上都表现出稳健的可推广性。我们引入了一种新颖的双线性注意机制（BAM），用于显式处理依赖信息，其操作是基于转换数据的协方差矩阵水平，并尊重对称正定矩阵流形的几何性质。实证评估显示了我们的方法在检测广泛范围的依赖关系中的稳健性，在无向图估计方面表现出优势，并通过一种新颖的两步方法在完成部分有向无环图估计中取得竞争优势。