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

2025-07-21

AI Summary

Existing community detection methods for single-cell RNA sequencing (scRNA-seq) data require pre-specifying the number of communities and suffer from instability under high noise or extreme sparsity. To address this, we propose a two-stage statistical inference framework: first, constructing a likelihood-based stochastic block model (SBM) network from scRNA-seq data; second, introducing a novel sequential multiple testing procedure to adaptively estimate the number of communities. The method is theoretically consistent, requires no prior knowledge of community count, and significantly improves robustness to technical noise and data sparsity. On multiple benchmark datasets, it achieves superior accuracy in estimating the true number of communities and yields higher-quality clustering compared to state-of-the-art approaches. Biologically, it successfully identifies five functionally distinct subpopulations among human retinal bipolar cells—demonstrating both quantitative performance gains and strong biological interpretability.

Technology Category

• Machine Learning: Semi-Supervised Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Estimating true number of communities in noisy scRNA-seq datasets
• Extracting suitable networks from scRNA-seq data effectively
• Developing a robust method for SBM community detection

Innovation

• Likelihood-based SBM extraction from scRNA-seq
• Sequential multiple testing for community estimation
• Consistent under moderate sparsity conditions