arXiv:2503.19554stat.MLcs.LG2025-03

无需已知因果图,通过推断目标变量的直接原因来优化结果。

Causal Bayesian Optimization with Unknown Graphs

  • 聚焦目标变量的直接因果父节点进行优化
  • 在线性情况下推导出后验分布闭式解
  • 适合因果结构未知但需高效优化的场景

因果贝叶斯优化(CBO)旨在通过有针对性的干预来优化目标变量,传统方法依赖于完整且准确的因果图,但在现实中常不可得。本文提出一种无需预先知晓因果图的新方法,理论分析表明仅关注目标变量的直接因果父节点即可实现有效优化,并通过实证验证了这一思路。我们引入一种基于贝叶斯后验的方法,用于学习目标变量的直接父节点,从而在优化过程中同步推断因果结构。在线性情形下,推导出后验分布的闭式解;在非线性情形下,采用高斯过程(GP)近似,仍可实现对目标变量父节点的推断与优化。该方法在多个基准上表现优异,且可扩展至大规模图结构,适用于因果信息不完整的实际场景。

原文摘要 · Abstract (English)

Causal Bayesian Optimization (CBO) is a methodology designed to optimize an outcome variable by leveraging known causal relationships through targeted interventions. Traditional CBO methods require a fully and accurately specified causal graph, which is a limitation in many real-world scenarios where such graphs are unknown. To address this, we propose a new method for the CBO framework that operates without prior knowledge of the causal graph. Consistent with causal bandit theory, we demonstrate through theoretical analysis and that focusing on the direct causal parents of the target variable is sufficient for optimization, and provide empirical validation in the context of CBO. Furthermore we introduce a new method that learns a Bayesian posterior over the direct parents of the target variable. This allows us to optimize the outcome variable while simultaneously learning the causal structure. Our contributions include a derivation of the closed-form posterior distribution for the linear case. In the nonlinear case where the posterior is not tractable, we present a Gaussian Process (GP) approximation that still enables CBO by inferring the parents of the outcome variable. The proposed method performs competitively with existing benchmarks and scales well to larger graphs, making it a practical tool for real-world applications where causal information is incomplete.

因果推断贝叶斯优化图学习

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