Causal discovery amounts to learning a directed acyclic graph (DAG) that encodes a causal model. This model selection problem can be challenging due to its large combinatorial search space, particularly when dealing with non-parametric causal models. Recent research has sought to bypass the combinatorial search by reformulating causal discovery as a continuous optimization problem, employing constraints that ensure the acyclicity of the graph. In non-parametric settings, existing approaches typically rely on finite-dimensional approximations of the relationships between nodes, resulting in a score-based continuous optimization problem with a smooth acyclicity constraint. In this work, we develop an alternative approximation method by utilizing reproducing kernel Hilbert spaces (RKHS) and applying general sparsity-inducing regularization terms based on partial derivatives. Within this framework, we introduce an extended RKHS representer theorem. To enforce acyclicity, we advocate the log-determinant formulation of the acyclicity constraint and show its stability. Finally, we assess the performance of our proposed RKHS-DAGMA procedure through simulations and illustrative data analyses.

本研究解决了非参数因果模型中有向无环图（DAG）的学习问题，考虑到其组合搜索空间的复杂性。通过引入再生核希尔伯特空间（RKHS）和基于偏导数的稀疏正则化，提出了一种新的近似方法，并加强了对图的无环性约束，显示出其良好的稳定性和性能。该方法可能影响因果发现领域，提高模型选择的效率。

基于核的可微学习非参数有向无环图模型