基于层级背景知识与潜在变量的约束因果发现：面向单一或重叠数据集 (Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets)

from arxiv, Accepted for the 4th Conference on Causal Learning and Reasoning (CLeaR 2025). Version 3: Corrected email addresses. Version 2: Corrected numbering in Example 1

In this paper we consider the use of tiered background knowledge within constraint based causal discovery. Our focus is on settings relaxing causal sufficiency, i.e. allowing for latent variables which may arise because relevant information could not be measured at all, or not jointly, as in the case of multiple overlapping datasets. We first present novel insights into the properties of the 'tiered FCI' (tFCI) algorithm. Building on this, we introduce a new extension of the IOD (integrating overlapping datasets) algorithm incorporating tiered background knowledge, the 'tiered IOD' (tIOD) algorithm. We show that under full usage of the tiered background knowledge tFCI and tIOD are sound, while simple versions of the tIOD and tFCI are sound and complete. We further show that the tIOD algorithm can often be expected to be considerably more efficient and informative than the IOD algorithm even beyond the obvious restriction of the Markov equivalence classes. We provide a formal result on the conditions for this gain in efficiency and informativeness. Our results are accompanied by a series of examples illustrating the exact role and usefulness of tiered background knowledge.

翻译：本文探讨了在基于约束的因果发现中应用层级背景知识的问题。我们重点关注放宽因果充分性假设的场景，即允许潜在变量的存在——这些变量可能因相关信息完全无法测量，或因多个重叠数据集的情况而无法联合测量。我们首先对“层级FCI”（tFCI）算法的性质提出了新的理论见解。在此基础上，我们提出了整合重叠数据集（IOD）算法的新扩展版本——融合层级背景知识的“层级IOD”（tIOD）算法。我们证明，在充分利用层级背景知识的前提下，tFCI与tIOD算法具有可靠性；而简化版本的tIOD与tFCI算法同时具备可靠性与完备性。进一步研究表明，即使超出马尔可夫等价类的显式约束范围，tIOD算法在多数情况下仍能比IOD算法显著提升效率与信息量。我们通过形式化结果明确了这种效率与信息增益的实现条件。所有理论结果均辅以系列示例，具体阐释了层级背景知识的确切作用与实用价值。