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.

翻译：在统计学与机器学习领域，检测数据集中的依赖关系是一项核心挑战。本文提出了一种用于监督图结构学习的新型神经网络模型，即学习观测数据与其底层依赖结构之间映射的过程。该模型通过形状及耦合关系可变的模拟输入数据进行训练，且推理时仅需对训练后的网络执行单次前向传播。通过利用结构方程模型并采用随机生成的多变量切比雪夫多项式模拟训练数据，我们的方法在线性依赖及各类非线性依赖场景下均展现出稳健的泛化能力。我们引入了一种新型双线性注意力机制（BAM），用于显式处理依赖信息。该机制作用于变换后数据的协方差矩阵层面，并遵循对称正定矩阵流形的几何特性。实验评估表明，该方法在检测多种依赖关系时具有鲁棒性，在无向图估计中表现卓越，并通过一种新颖的两步法在完全部分有向无环图估计中展现出竞争力。