Almost Optimal Universal Lower Bound for Learning Causal DAGs with Atomic Interventions

INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 151(2022)

引用 2|浏览12
暂无评分
摘要
A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected edges have to be oriented using interventions, which can be very expensive to perform in applications. Thus, the problem of minimizing the number of interventions needed to fully orient the MEC has received a lot of recent attention, and is also the focus of this work. We prove two main results. The first is a new universal lower bound on the number of atomic interventions that any algorithm (whether active or passive) would need to perform in order to orient a given MEC. Our second result shows that this bound is, in fact, within a factor of two of the size of the smallest set of atomic interventions that can orient the MEC. Our lower bound is provably better than previously known lower bounds. The proof of our lower bound is based on the new notion of clique-block shared-parents (CBSP) orderings, which are topological orderings of DAGs without v-structures and satisfy certain special properties. Further, using simulations on synthetic graphs and by giving examples of special graph families, we show that our bound is often significantly better.
更多
查看译文
关键词
causal dags,atomic interventions,optimal universal lower bound,learning
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要