Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scores
利用似然比评分序贯学习因果图的拓扑排序AI 解读 ↓
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利用似然比评分序贯学习因果图的拓扑排序
- 研究问题
- 在允许一般误差分布的条件下，能否通过逐个确定变量顺序识别因果有向无环图，并使排序算法适用于高维节点集合？
- 方法与思路
- 作者从根节点开始逐步排序，在每一步对回归残差计算简单似然比评分，以决定下一节点，并讨论总体识别与算法复杂度。
- 材料陈述的贡献
- 摘要称总体程序在温和条件下识别真实拓扑排序，复杂度为节点数乘最大邻域规模；数值实验展示大规模表现并包含单细胞应用。
- 阅读关注点
- 应核对一般误差分布下的具体识别限制、似然比评分与回归步骤，以及总体排序保证能否转化为样本保证和复杂度计算的前提。
- 阅读边界
- 所给版本为 arXiv 预印本，未核实同行评审或接收；摘要未列所谓温和假设或有限样本误差界，不能认为任意误差分布均可识别。
原文摘要
Causal discovery, the learning of causality in a data mining scenario, has been of strong scientific and theoretical interest as a starting point to identify "what causes what?" Contingent on assumptions and a proper learning algorithm, it is sometimes possible to identify and accurately estimate a causal directed acyclic graph (DAG), as opposed to a Markov equivalence class of graphs that gives ambiguity of causal directions. The focus of this paper is in highlighting the identifiability and estimation of DAGs with general error distributions through a general sequential sorting procedure that orders variables one at a time, starting at root nodes, followed by children of the root nodes, and so on until completion. We demonstrate a novel application of this general approach to estimate the topological ordering of a DAG. At each step of the procedure, only simple likelihood ratio scores are calculated on regression residuals to decide the next node to append to the current partial ordering. The computational complexity of our algorithm on a p-node problem is O(pd), where d is the maximum neighborhood size. Under mild assumptions, the population version of our procedure provably identifies a true ordering of the underlying DAG. We provide extensive numerical evidence to demonstrate that this sequential procedure scales to possibly thousands of nodes and works well for high-dimensional data. We accompany these numerical experiments with an application to a single-cell gene expression dataset.