Provable Guarantees and Efficient Learning of Structural Equation Models with Latent Confounders

2026-09-16

AI Summary

本文针对存在潜在混淆变量时因果关系发现的问题，提出了一种通过恢复观测变量的精度矩阵为稀疏加低秩矩阵的方法来重建观测变量间的有向无环图。

Abstract

Causal discovery aims to recover causal relationships from observed data. In various fields, exploring causal relationships among variables remains an important topic, but this task becomes challenging due to the existence of latent confounders. Ignoring such confounders can lead to false associations and incorrect edge directions. In this paper, we study the linear structural equation model with latent confounders. We propose an algorithm that iteratively identifies terminal (observed) nodes and reconstructs the directed acyclic graph of the observed variables. To do this, we recover the precision matrix of the observed variables as a sparse plus low-rank matrix: a sparse matrix captures the conditional dependencies among observed variables, while a low-rank matrix captures the combined influence of a few latent confounders. We establish that for $p$ observed variables, $r$ latent confounders and $s$ edges, our procedure correctly identifies the directed causal relationship among observed variables, for $n \gtrsim \max\{s\log p,\ r p\}$ samples. Experimental results validate our theoretical contributions.

Problem

• causal discovery
• latent confounders
• structural equation model

Innovation

• latent confounders
• sparse plus low-rank matrix
• directed acyclic graph
• causal discovery