Latent Hierarchical Causal Structure Discovery with Rank Constraints
Biwei Huang ∗1 Charles Low 1, Feng Xie3, Clark Glymour1, Kun Zhang1,2 1 Carnegie Mellon University 2 Mohamed bin Zayed University of Artificial Intelligence 3 Beijing Technology and Business University, China {bwei.huang, charleslow88, These authors contributed equally to this work. Accepted at 36th Conference on Neural Information Processing Systems (NeurIPS 2022).
Abstract
Most causal discovery procedures assume that there are no latent confounders in the system, which is often violated in real-world problems. In this paper, we consider a challenging scenario for causal structure identification, where some variables are latent and they form a hierarchical graph structure to generate the measured variables; the children of latent variables may still be latent and only leaf nodes are measured, and moreover, there can be multiple paths between every pair of variables (i.e., it is beyond tree structure). We propose an estimation procedure that can efficiently locate latent variables, determine their cardinalities, and identify the latent hierarchical structure, by leveraging rank deficiency constraints over the measured variables. We show that the proposed algorithm can find the correct Markov equivalence class of the whole graph asymptotically under proper restrictions on the graph structure.
中文速览
真实世界的数据里往往存在我们观测不到的"幕后变量"（潜变量，latent variables），它们以层级结构相互影响并最终生成我们能测量到的数据，忽视这些潜变量会导致错误的因果推断。已有方法要么只能处理树形结构（每对变量间只有唯一路径），要么要求每个潜变量必须直接拥有足够多的可观测子节点，限制太强。本文提出了一种新算法，利用可观测变量协方差矩阵的"秩亏缺"（rank deficiency）性质——即当某组潜变量恰好将两组可观测变量d-分离时，对应的互协方差矩阵秩会下降——来自动定位潜变量、确定其数量（基数），并还原整个层级因果图结构，且允许变量之间存在多条路径。理论上证明了在"不可约线性潜层级图"和秩忠实性条件下，算法能渐近地恢复整个图的马尔可夫等价类；合成数据实验也验证了方法的有效性。这项工作将潜变量因果发现从受限的树形结构推广到更一般的层级图，为复杂系统中的因果结构学习提供了更实用的工具。
原文 arXiv:2210.01798;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2210.01798v1