Selective Inference for Hierarchical Clustering

TL;DR

This paper introduces a selective inference method for testing differences in means between clusters identified by hierarchical clustering, controlling for inflated false positives due to data-driven group selection.

Contribution

It develops an exact p-value computation approach for hierarchical clustering, addressing the bias introduced by data-dependent group formation.

Findings

Controls type I error in clustering-based tests

Provides exact p-values for hierarchical clustering

Demonstrates effectiveness on simulated and real data

Abstract

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.