Multiple Hypothesis Testing To Estimate The Number Of Communities in Stochastic Block Models

TL;DR

This paper introduces a new statistical method combining likelihood-based network extraction and sequential multiple testing to accurately estimate the number of communities in stochastic block models, especially for noisy scRNA-seq data.

Contribution

It presents a novel sequential multiple testing approach for estimating community numbers in SBMs, with proven consistency and competitive performance on benchmark datasets.

Findings

SMT method is consistent under moderate sparsity.

Our approach outperforms existing methods on benchmark datasets.

Application to real scRNA-seq data reveals meaningful cell subgroups.

Abstract

Clustering of single-cell RNA sequencing (scRNA-seq) datasets can give key insights into the biological functions of cells. Therefore, it is not surprising that network-based community detection methods (one of the better clustering methods) are increasingly being used for the clustering of scRNA-seq datasets. The main challenge in implementing network-based community detection methods for scRNA-seq datasets is that these methods \emph{apriori} require the true number of communities or blocks for estimating the community memberships. Although there are existing methods for estimating the number of communities, they are not suitable for noisy scRNA-seq datasets. Moreover, we require an appropriate method for extracting suitable networks from scRNA-seq datasets. For addressing these issues, we present a two-fold solution: i) a simple likelihood-based approach for extracting stochastic block models (SBMs) out of scRNA-seq datasets, ii) a new sequential multiple testing (SMT) method for estimating the number of communities in SBMs. We study the theoretical properties of SMT and establish its consistency under moderate sparsity conditions. In addition, we compare the numerical performance of the SMT with several existing methods. We also show that our approach performs competitively well against existing methods for estimating the number of communities on benchmark scRNA-seq datasets. Finally, we use our approach for estimating subgroups of a human retina bipolar single cell dataset.