MACSL: A gradient-based multi-label acyclic causal structure learner

doi:10.1016/j.patcog.2026.114443

MACSL: A gradient-based multi-label acyclic causal structure learner

2026-07-01

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DOI：10.1016/j.patcog.2026.114443

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Causal structure learning aims to uncover the underlying directed acyclic graph that governs dependencies among variables, providing interpretable insights and supporting robust decision-making. However, most existing methods rely on conditional independence (CI) tests, which often suffer from the faithfulness assumption. Although recent optimization-based methods avoid CI tests, they are typically limited to covariateonly or single-label settings. When applied to multi-label scenarios, these methods fail to capture the complex dependencies between features and multi-labels. To address these issues, we propose MACSL, a Gradient-based Multi-label Acyclic Causal Structure Learner that jointly models feature-feature, feature-label and label-label dependencies through learnable causal matrices. Specifically, MACSL introduces a polynomial-approximation-based acyclicity constraint and optimizes a unified objective that combines prediction, reconstruction, and dependency modeling. We theoretically demonstrate that MACSL can recover causal relations even when the faithfulness assumption is violated. Experiments on synthetic and real-world datasets illustrate its superior performance in both causal structure learning and interpretable feature selection. The code is available at https://github.com/malinjlu/MACSL.

Keywords:

Causal structure learning

Causal feature selection

Multi-label learning

Markov blanket

MACSL: A gradient-based multi-label acyclic causal structure learner

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