Koen Van den Berge | Searcharxiv

arXiv2023

Structure learning for zero-inflated counts, with an application to single-cell RNA sequencing data

The problem of estimating the structure of a graph from observed data is of growing interest in the context of high-throughput genomic data, and single-cell RNA sequencing in particular. These, however, are challenging applications, since the data consist of high-dimensional counts with high variance and over-abundance of zeros. Here, we present a general framework for learning the structure of a graph from single-cell RNA-seq data, based on the zero-inflated negative binomial distribution. We demonstrate with simulations that our approach is able to retrieve the structure of a graph in a variety of settings and we show the utility of the approach on real data.

q-bio.GN↗

arXiv2020

Hierarchical community detection by recursive partitioning

The problem of community detection in networks is usually formulated as finding a single partition of the network into some "correct" number of communities. We argue that it is more interpretable and in some regimes more accurate to construct a hierarchical tree of communities instead. This can be done with a simple top-down recursive partitioning algorithm, starting with a single community and separating the nodes into two communities by spectral clustering repeatedly, until a stopping rule suggests there are no further communities. This class of algorithms is model-free, computationally efficient, and requires no tuning other than selecting a stopping rule. We show that there are regimes where this approach outperforms K-way spectral clustering, and propose a natural framework for analyzing the algorithm's theoretical performance, the binary tree stochastic block model. Under this model, we prove that the algorithm correctly recovers the entire community tree under relatively mild assumptions. We apply the algorithm to a gene network based on gene co-occurrence in 1580 research papers on anemia, and identify six clusters of genes in a meaningful hierarchy. We also illustrate the algorithm on a dataset of statistics papers.

stat.ME↗