Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models
<|reference_start|>Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models: 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.<|reference_end|>
@article{liang2024kernel-based,
    title={Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic
  Graphical Models},
    author={Yurou Liang, Oleksandr Zadorozhnyi and Mathias Drton},
    journal={arXiv preprint arXiv:2408.10976},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.10976},
    primaryClass={stat.ML cs.LG}
}