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

TL;DR

This paper introduces a novel kernel-based method for learning non-parametric causal DAGs by reformulating the problem as a continuous optimization with a new acyclicity constraint, enabling more flexible causal discovery.

Contribution

It develops an RKHS-based approximation for causal discovery, introduces an extended RKHS representer theorem, and employs a log-determinant acyclicity constraint for improved stability.

Findings

Demonstrates the effectiveness of the RKHS-DAGMA method through simulations.

Shows improved stability and flexibility over existing approaches.

Provides illustrative data analyses validating the approach.

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.