  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.
