Causal Discovery in Linear Latent Variable Models Subject to Measurement Error
Causal Discovery in Linear Latent Variable Models Subject to Measurement Error
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DOI：
10.48550/arxiv.2211.03984
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发表时间：
2022-11
期刊：
影响因子：
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通讯作者：
Yuqin Yang;AmirEmad Ghassami;Mohamed S. Nafea;N. Kiyavash;Kun Zhang;I. Shpitser
中科院分区：
文献类型：
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作者：
Yuqin Yang;AmirEmad Ghassami;Mohamed S. Nafea;N. Kiyavash;Kun Zhang;I. Shpitser
我们专注于线性系统中存在测量误差时的因果发现，其中混合矩阵（即指示与观测变量相关的独立外生噪声项的矩阵）被识别到列的排列和缩放。我们证明了在存在未观察到的无父原因的情况下，该问题与因果发现之间存在某种令人惊讶的联系，从某种意义上说，在这些问题中要推断的基础模型之间存在由混合矩阵给出的映射。因此，基于一个模型的混合矩阵的任何可识别性结果都会转换为另一模型的可识别性结果。我们描述了在两部分忠实性假设下可以在多大程度上识别因果模型。仅在假设的第一部分（对应于忠实度的传统定义）下，可以学习结构直到变量的有序分组之间的因果排序，但不能识别跨组的所有边缘。我们进一步表明，如果忠实度假设的两个部分都被施加，则可以将结构学习到更精细的有序分组。作为这种细化的结果，对于具有未观察到的无父母原因的潜变量模型，可以识别其结构。根据我们的理论结果，我们为这两种模型提出了因果结构学习方法，并评估了它们在合成数据上的性能。
We focus on causal discovery in the presence of measurement error in linear systems where the mixing matrix, i.e., the matrix indicating the independent exogenous noise terms pertaining to the observed variables, is identified up to permutation and scaling of the columns. We demonstrate a somewhat surprising connection between this problem and causal discovery in the presence of unobserved parentless causes, in the sense that there is a mapping, given by the mixing matrix, between the underlying models to be inferred in these problems. Consequently, any identifiability result based on the mixing matrix for one model translates to an identifiability result for the other model. We characterize to what extent the causal models can be identified under a two-part faithfulness assumption. Under only the first part of the assumption (corresponding to the conventional definition of faithfulness), the structure can be learned up to the causal ordering among an ordered grouping of the variables but not all the edges across the groups can be identified. We further show that if both parts of the faithfulness assumption are imposed, the structure can be learned up to a more refined ordered grouping. As a result of this refinement, for the latent variable model with unobserved parentless causes, the structure can be identified. Based on our theoretical results, we propose causal structure learning methods for both models, and evaluate their performance on synthetic data.