Goodness-of-fit tests for linear non-Gaussian structural equation models
线性非高斯结构方程模型的拟合优度检验AI 解读 ↓
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线性非高斯结构方程模型的拟合优度检验
- 研究问题
- 因果发现依赖线性非高斯结构方程假设时，如何检验这一假设是否符合数据，并兼顾存在与不存在潜在混杂的情形？
- 方法与思路
- 作者利用线性结构对二阶及高阶矩施加的矩阵和张量秩约束，采用不完全 U 统计量、乘子自助法和奇异值渐近近似。
- 材料陈述的贡献
- 摘要称建立了无潜在混杂及含潜在混杂模型的拟合优度检验，并通过因果配对基准数据展示这些方法的应用。
- 阅读关注点
- 应核对矩约束究竟检验哪些模型性质、所需矩条件，以及潜在混杂扩展、子行列式估计和零分布近似的适用范围。
- 阅读边界
- 仅据所给 Crossref 摘要，不能认定未拒绝模型就证明因果方向正确；检验一致性范围、样本要求与数值表现未说明。
原文摘要
Abstract The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations identifiable. One prominent assumption is that the joint distribution of the observed variables follows a linear non-Gaussian structural equation model. In this paper, we develop novel goodness-of-fit tests that assess the validity of this assumption in the basic setting without latent confounders, as well as in extension to linear models that incorporate latent confounders. Our approach involves testing algebraic relations among second and higher moments that hold as a consequence of the linearity of the structural equations. Specifically, we show that the linearity implies rank constraints on matrices and tensors derived from moments. For a practical implementation of our tests, we consider a multiplier bootstrap method that uses incomplete $ U $-statistics to estimate subdeterminants, as well as asymptotic approximations to the null distribution of singular values. The methods are illustrated, in particular, for the Tübingen collection of benchmark datasets on cause-effect pairs.