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

MCML Authors

Mathias Drton

Prof. Dr.

Principal Investigator

Mathematical Statistics

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.

inproceedings

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PGM 2024

12th International Conference on Probabilistic Graphical Models. Nijmegen, The Netherlands, Sep 11-13, 2024.

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Authors

Y. Liang • O. Zadorozhnyi • M. Drton

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Links

URL

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Research Area

 A1 | Statistical Foundations & Explainability