Selective Inference for Hierarchical Clustering

• URL: http://arxiv.org/abs/2012.02936v1
• Date: Sat, 5 Dec 2020 03:03:19 GMT
• Title: Selective Inference for Hierarchical Clustering
• Authors: Lucy L. Gao, Jacob Bien and Daniela Witten
• Abstract summary: We propose a selective inference approach to test for a difference in means between two clusters obtained from any clustering method. Our procedure controls the selective Type I error rate by accounting for the fact that the null hypothesis was generated from the data.
• Score: 2.3311605203774386
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Testing for a difference in means between two groups is fundamental to answering research questions across virtually every scientific area. Classical tests control the Type I error rate when the groups are defined a priori. However, when the groups are instead defined via a clustering algorithm, then applying a classical test for a difference in means between the groups 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 obtained from any clustering method. Our procedure controls the selective Type I error rate by accounting for the fact that the null hypothesis was generated from 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-seq data.

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