Selective Inference for Hierarchical Clustering
This work provides a method for statisticians and data scientists to perform valid hypothesis testing on groups discovered through hierarchical clustering, preventing erroneous conclusions.
This paper addresses the inflated Type I error rate when performing classical tests for a difference in means after groups have been defined by clustering. The authors propose a selective inference approach that controls the selective Type I error rate by accounting for data-driven hypothesis selection, enabling efficient computation of exact p-values for agglomerative hierarchical clustering.
Classical tests for a difference in means control the type I error rate when the groups are defined a priori. However, when the groups are instead defined via clustering, then applying a classical test yields an extremely inflated type I error rate. Notably, this problem persists even if two separate and independent data sets are used to define the groups and to test for a difference in their means. To address this problem, in this paper, we propose a selective inference approach to test for a difference in means between two clusters. Our procedure controls the selective type I error rate by accounting for the fact that the choice of null hypothesis was made based on the data. We describe how to efficiently compute exact p-values for clusters obtained using agglomerative hierarchical clustering with many commonly-used linkages. We apply our method to simulated data and to single-cell RNA-sequencing data.