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Optimal Permutation Recovery in Permuted Monotone Matrix Model

Motivated by recent research on quantifying bacterial growth dynamics based on genome assemblies, we consider a permuted monotone matrix model Y=ΘΠ+Z , 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.

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Informasi Detail

Judul Seri

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION (JASA); Vol.116 No.535 September 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1358 - 1372

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

SORTING
KENDALL’S TAU
MINIMAX LOWER BOUND
MICROBIOME GROWTH DYNAMICS

Info Detail Spesifik

https://doi.org/10.1080/01621459.2020.1713794

Pernyataan Tanggungjawab

Rong Ma, T. Tony Cai, Hongzhe Li

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