Optimal Permutation Recovery in Permuted Monotone Matrix Model

• Published in: Journal of the American Statistical Association Vol. 116; no. 535; pp. 1358 - 1372
• Main Authors: Ma, Rong, Tony Cai, T., Li, Hongzhe
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 2021; Taylor & Francis Ltd
• Subjects: Assemblies; Bacteria; Datasets; Genomes; Genomics; Kendall's tau; Microbiome growth dynamics; Minimax lower bound; Sorting; Mathematical analysis; Matrices (mathematics); Minimax technique; Noise; Permutations; Recovery; Regression analysis; Simulation; Statistical methods; Statistics; Microbiome growth dynamics; Minimax lower bound; Kendall’s tau; Sorting
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2020.1713794

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, Θ is an unknown mean matrix with monotone entries for each row, Π is a permutation matrix that permutes the columns of Θ, and Z is a noise matrix. This article studies the problem of estimation/recovery of Π 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.
Supplementary materials
for this article are available online.