Causal Discovery with Generalized Linear Models through Peeling Algorithms
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通过剥离算法实现广义线性模型的因果发现
- 研究问题
- 面对离散、连续及混合结果变量，并存在未观测混杂时，如何利用工具变量信息恢复祖先关系和直接的父子因果关系？
- 方法与思路
- 作者提出自下而上和自上而下的剥离算法：先用逐节点GLM回归恢复祖先超图，再借助父节点模型信息处理混杂并估计直接效应。
- 材料陈述的贡献
- 摘要称，论文给出模型可识别条件及关系恢复的统计保证，并通过数值实验和阿尔茨海默病基因调控网络应用展示方法。
- 阅读关注点
- 应核对工具变量有效性如何确定、未观测混杂允许何种结构，以及祖先超图到直接因果关系的恢复条件和误差传播。
- 阅读边界
- 这是arXiv预印本，同行评审或接收状态未核实；摘要未列明识别条件，且比较对象为不含混杂的结构学习方法，适用性需核对。
原文摘要
This article presents a novel method for causal discovery with generalized structural equation models suited for analyzing diverse types of outcomes, including discrete, continuous, and mixed data. Causal discovery often faces challenges due to unmeasured confounders that hinder the identification of causal relationships. The proposed approach addresses this issue by developing two peeling algorithms (bottom-up and top-down) to ascertain causal relationships and valid instruments. This approach first reconstructs a super-graph to represent ancestral relationships between variables, using a peeling algorithm based on nodewise GLM regressions that exploit relationships between primary and instrumental variables. Then, it estimates parent-child effects from the ancestral relationships using another peeling algorithm while deconfounding a child's model with information borrowed from its parents' models. The article offers a theoretical analysis of the proposed approach, which establishes conditions for model identifiability and provides statistical guarantees for accurately discovering parent-child relationships via the peeling algorithms. Furthermore, the article presents numerical experiments showcasing the effectiveness of our approach in comparison to state-of-the-art structure learning methods without confounders. Lastly, it demonstrates an application to Alzheimer's disease (AD), highlighting the utility of the method in constructing gene-to-gene and gene-to-disease regulatory networks involving Single Nucleotide Polymorphisms (SNPs) for healthy and AD subjects.