Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models

• URL: http://arxiv.org/abs/2408.10976v1
• Date: Tue, 20 Aug 2024 16:09:40 GMT
• Title: Kernel-Based Differentiable Learning of Non-Parametric Directed Acyclic Graphical Models
• Authors: Yurou Liang, Oleksandr Zadorozhnyi, Mathias Drton,
• Abstract summary: Causal discovery amounts to learning a directed acyclic graph (DAG) that encodes a causal model. Recent research has sought to bypass the search by reformulating causal discovery as a continuous optimization problem.
• Score: 17.52142371968811
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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