偏相关检验中的超曲面及其奇异性
Hypersurfaces and their singularities in partial correlation testing
摘要：
本文提出了一种计算有向高斯图模型参数空间中区域体积的渐近理论，这些区域是由有界偏相关得到的。我们研究这些卷使用的方法，从代数几何的实对数正则阈值。我们的分析涉及相关超曲面的奇异轨迹的计算。统计应用包括PC算法的强忠实性假设，以及因果推理中混淆偏倚的量化。对树、蝴蝶结图、三部图和完全图进行了详细的分析。
英文摘要：
An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC-algorithm, and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow-ties, tripartite graphs, and complete graphs.
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