Post-clustering difference testing: valid inference and practical considerations

Benjamin Hivert (1, 2, 3) , Denis Agniel (4) , Rodolphe Thiébaut (2, 3, 1, 5) , Boris P. Hejblum (1, 2, 3)

1 BPH - Bordeaux population health
2 SISTM - Statistics In System biology and Translational Medicine
3 VRI - Vaccine Research Institute [Créteil, France]
4 Rand Corporation
5 CHU Bordeaux

Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to infer the variables that significantly separate the estimated clusters from each other. However, data-driven hypotheses are considered for the inference process, since the hypotheses are derived from the clustering results. This double use of the data leads traditional hypothesis test to fail to control the Type I error rate particularly because of uncertainty in the clustering process and the potential artificial differences it could create. We propose three novel statistical hypothesis tests which account for the clustering process. Our tests efficiently control the Type I error rate by identifying only variables that contain a true signal separating groups of observations.

Keywords: Clustering; hypothesis testing; double-dipping; circular analysis; selective inference; multimodality test; Dip Test

Domains: Methodology [stat.ME]

Benjamin Hivert, Denis Agniel, Rodolphe Thiébaut, Boris P. Hejblum. Post-clustering difference testing: valid inference and practical considerations. Computational Statistics and Data Analysis, 2024, 193, pp.107916. ⟨10.1016/j.csda.2023.107916⟩. ⟨hal-03889565⟩