Optimal estimation of bacterial growth rates based on a permuted monotone matrix

• 成果类型: Article
• 署名作者: Ma, Rong; Cai, T. Tony; Li, Hongzhe
• 署名单位: University of Pennsylvania; University of Pennsylvania
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaa082
• 发表日期: 2021
• 页码: 693708
• 关键词: Empirical Bayes; read alignment; replication

摘要

Motivated by the problem of estimating bacterial growth rates for genome assemblies from shotgun metagenomic data, we consider the permuted monotone matrix model Y = Theta Pi + Z where Y is an element of R-nxp is observed, Theta is an element of R-nxp an unknown approximately rank-one signal matrix with monotone rows, Pi is an element of R-pxp is an unknown permutation matrix, and Z is an element of R-nxp is the noise matrix. In this article we study estimation of the extreme values associated with the signal matrix Theta, including its first and last columns and their difference. Treating these estimation problems as compound decision problems, minimax rate-optimal estimators are constructed using the spectral column-sorting method. Numerical experiments on simulated and synthetic microbiome metagenomic data are conducted, demonstrating the superiority of the proposed methods over existing alternatives. The methods are illustrated by comparing the growth rates of gut bacteria in inflammatory bowel disease patients and control subjects.