Optimal rates of statistical seriation
Name
1607.02435.pdf
Description
Submitted version
Size
739.48 KB
Format
Adobe PDF
Checksum (MD5)
dd5dc8c82e6845f4da2eb4a7fd9e8b42
Author(s)
Mao, Cheng
Rigollet, Philippe
Date Issued
2019
Journal
Bernoulli
Publisher
Bernoulli Society for Mathematical Statistics and Probability
Citation
Flammarion, Nicolas, Cheng Mao and Philippe Rigollet. “Optimal rates of statistical seriation.” Bernoulli, 25, 1 (2019): 623-653 © 2019 The Author(s)
Version
Original manuscript
Abstract
Given a matrix, the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of interest is observed with noise and study the corresponding minimax rate of estimation of the matrices. Specifically, when the columns are either unimodal or monotone, we show that the least squares estimator is optimal up to logarithmic factors and adapts to matrices with a certain natural structure. Finally, we propose a computationally efficient estimator in the monotonic case and study its performance both theoretically and experimentally. Our work is at the intersection of shape constrained estimation and recent work that involves permutation learning, such as graph denoising and ranking.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.3150/17-BEJ1000
