Half-Trek Criterion for Identifiability of Latent Variable Models
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潜变量模型可识别性的半路径准则
- 研究问题
- 研究在线性结构方程模型包含潜变量时，能否仅根据可观测变量的协方差矩阵识别这些变量之间的直接因果效应。
- 方法与思路
- 作者在未经潜变量投影的原始图模型上构造潜因子半路径准则，并讨论将潜变量子集搜索规模限制后的验证复杂度。
- 材料陈述的贡献
- 摘要称，新准则是有理可识别性的充分条件，可处理潜变量影响广泛的情形；限制搜索子集大小后，可在图规模的多项式时间内验证。
- 阅读关注点
- 应核对图模型及噪声限制、可识别性命题的精确范围、协方差恢复公式，以及搜索规模限制是否影响准则的识别覆盖范围。
- 阅读边界
- 这是预印本，同行评审或期刊接收未核实。摘要未给出完整条件与证明，充分准则未通过也不能据此判定模型不可识别。
原文摘要
We consider linear structural equation models with latent variables and develop a criterion to certify whether the direct causal effects between the observable variables are identifiable based on the observed covariance matrix. Linear structural equation models assume that both observed and latent variables solve a linear equation system featuring stochastic noise terms. Each model corresponds to a directed graph whose edges represent the direct effects that appear as coefficients in the equation system. Prior research has developed a variety of methods to decide identifiability of direct effects in a latent projection framework, in which the confounding effects of the latent variables are represented by correlation among noise terms. This approach is effective when the confounding is sparse and effects only small subsets of the observed variables. In contrast, the new latent-factor half-trek criterion (LF-HTC) we develop in this paper operates on the original unprojected latent variable model and is able to certify identifiability in settings, where some latent variables may also have dense effects on many or even all of the observables. Our LF-HTC is an effective sufficient criterion for rational identifiability, under which the direct effects can be uniquely recovered as rational functions of the joint covariance matrix of the observed random variables. When restricting the search steps in LF-HTC to consider subsets of latent variables of bounded size, the criterion can be verified in time that is polynomial in the size of the graph.