Inferring Independent Sets of Gaussian Variables after Thresholding Correlations
研究了从数据中选出与所有其他变量相关性低于阈值的高斯变量集后，如何检验该集是否独立于其余变量，并提出了一个避免过度保守的新检验方法。
We consider testing whether a set of Gaussian variables, selected from the data, is independent of the remaining variables. This set is selected via a very simple approach: these are the variables for which the correlation with all other variables falls below some threshold. Unlike other settings in selective inference, failure to account for the selection step leads to excessively conservative (as opposed to anti-conservative) results. We propose a new test that conditions on the event that the selection resulted in the set of variables in question, and thus is not overly conservative. To achieve computational tractability, we develop a characterization of the conditioning event in terms of the canonical correlation between groups of random variables. In simulation studies and in the analysis of gene co-expression networks, we show that our approach has much higher power than a “naive” approach that ignores the effect of selection. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.