论文标题
基于三重互动的忠实忠诚假设
A Weaker Faithfulness Assumption based on Triple Interactions
论文作者
论文摘要
因果发现中的核心假设之一是忠实的假设，即假设数据中发现的独立性是由于真实因果图中的分离所致。但是，可以通过多种方式违反此假设，包括XOR连接，确定性功能或取消路径。在这项工作中，我们提出了一个较弱的假设，即我们称为$ 2 $ -Adjacency的忠诚。与毗邻的忠诚相反，假设在因果图中连接的每对变量之间没有条件独立性，我们只需要一个节点和其Markov毯子的子集之间的有条件独立性，最多包含两个节点。同等地，我们适应了这种环境的忠诚。我们进一步提出了适用于弱假设下的因果发现的合理定位规则。作为概念的证明，我们得出了一种经过改进的增长和收缩算法，该算法恢复了目标节点的马尔可夫毯子，并在严格的弱假设下证明了其正确性，而不是标准的忠实假设。
One of the core assumptions in causal discovery is the faithfulness assumption, i.e., assuming that independencies found in the data are due to separations in the true causal graph. This assumption can, however, be violated in many ways, including xor connections, deterministic functions or cancelling paths. In this work, we propose a weaker assumption that we call $2$-adjacency faithfulness. In contrast to adjacency faithfulness, which assumes that there is no conditional independence between each pair of variables that are connected in the causal graph, we only require no conditional independence between a node and a subset of its Markov blanket that can contain up to two nodes. Equivalently, we adapt orientation faithfulness to this setting. We further propose a sound orientation rule for causal discovery that applies under weaker assumptions. As a proof of concept, we derive a modified Grow and Shrink algorithm that recovers the Markov blanket of a target node and prove its correctness under strictly weaker assumptions than the standard faithfulness assumption.
