Towards Optimal Estimation of Bivariate Isotonic Matrices with Unknown Permutations
Abstract
Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating an unknown matrix in this class, based on noisy observations of (possibly, a subset of) its entries. We design and analyze polynomial-time algorithms that improve upon the state of the art in two distinct metrics, showing, in particular, that minimax optimal, computationally efficient estimation is achievable in certain settings. Along the way, we prove matching upper and lower bounds on the minimax radii of certain cone testing problems, which may be of independent interest.
Cite
@article{arxiv.1806.09544,
title = {Towards Optimal Estimation of Bivariate Isotonic Matrices with Unknown Permutations},
author = {Cheng Mao and Ashwin Pananjady and Martin J. Wainwright},
journal= {arXiv preprint arXiv:1806.09544},
year = {2019}
}
Comments
60 pages, 1 figure. This paper is a longer version of the paper arXiv:1802.09963 v3, which appeared in part as a 4-page extended abstract at Conference on Learning Theory (COLT) 2018. This paper studies the problem in more general settings and in another error metric. This version corrects a statement in Theorem 2 of v1