We introduce a new Collaborative Causal Discovery problem, through which we model a common scenario in which we have multiple independent entities each with their own causal graph, and the goal is to simultaneously learn all these causal graphs. We study this problem without the causal sufficiency assumption, using Maximal Ancestral Graphs (MAG) to model the causal graphs, and assuming that we have the ability to actively perform independent single vertex (or atomic) interventions on the entities. If the $M$ underlying (unknown) causal graphs of the entities satisfy a natural notion of clustering, we give algorithms that leverage this property and recovers all the causal graphs using roughly logarithmic in $M$ number of atomic interventions per entity. These are significantly fewer than $n$ atomic interventions per entity required to learn each causal graph separately, where $n$ is the number of observable nodes in the causal graph. We complement our results with a lower bound and discuss various extensions of our collaborative setting.
翻译:我们引入了一个新的合作因果关系发现问题, 通过这个问题, 我们模拟了一个共同的假设方案, 我们每个实体都有多个独立的实体, 都有各自的因果图表, 目标是同时学习所有这些因果图表。 我们研究这个问题时没有因果充足性假设, 使用Maximal 祖传图( MAG) 来模拟因果图表, 假设我们有能力对这些实体积极执行独立的单一顶点( 或原子) 干预措施。 如果这些实体的( 未知的) 基本因果图表满足了自然的集群概念, 我们给出算法, 利用这些属性, 并用每个实体大约对数的原子干预数量来回收所有因果图表。 这些算法远远少于每个实体所需的原子干预, 以分别学习每种因果图表, 其中美元是因果图中可观测的节点的数量。 我们用较低约束的速率来补充我们的结果, 并讨论我们协作环境的各种扩展。