Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models
This work addresses causal discovery in non-parametric settings, which is important for researchers in statistics and machine learning, but it appears incremental as it builds on existing continuous optimization approaches.
The authors tackled the problem of causal discovery for non-parametric directed acyclic graphical models by developing a kernel-based method with sparsity regularization and a stable acyclicity constraint, resulting in the RKHS-DAGMA procedure evaluated through simulations and data analyses.
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.