Optimal Permutation Recovery in Permuted Monotone Matrix Model

• 成果类型: Article
• 署名作者: Ma, Rong; Tony Cai, T.; Li, Hongzhe
• 署名单位: University of Pennsylvania; University of Pennsylvania
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2020.1713794
• 发表日期: 2021
• 页码: 1358-1372
• 关键词: optimal rates; replication; perturbation; microbiome; bacterial; bounds

摘要

Motivated by recent research on quantifying bacterial growth dynamics based on genome assemblies, we consider a permuted monotone matrix model , where the rows represent different samples, the columns represent contigs in genome assemblies and the elements represent log-read counts after preprocessing steps and Guanine-Cytosine (GC) adjustment. In this model, Theta is an unknown mean matrix with monotone entries for each row, pi is a permutation matrix that permutes the columns of Theta, and Z is a noise matrix. This article studies the problem of estimation/recovery of pi given the observed noisy matrix Y. We propose an estimator based on the best linear projection, which is shown to be minimax rate-optimal for both exact recovery, as measured by the 0-1 loss, and partial recovery, as quantified by the normalized Kendall's tau distance. Simulation studies demonstrate the superior empirical performance of the proposed estimator over alternative methods. We demonstrate the methods using a synthetic metagenomics dataset of 45 closely related bacterial species and a real metagenomic dataset to compare the bacterial growth dynamics between the responders and the nonresponders of the IBD patients after 8 weeks of treatment. for this article are available online.