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December 2020 Towards optimal estimation of bivariate isotonic matrices with unknown permutations
Cheng Mao, Ashwin Pananjady, Martin J. Wainwright
Ann. Statist. 48(6): 3183-3205 (December 2020). DOI: 10.1214/19-AOS1925

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. (A corollary of Theorem 3.5 of this paper was presented at the Conference on Learning Theory (COLT) 2018, and a statement of this result appears in the abstract (In Proceedings of the 31st Conference On Learning Theory (2018) 2037–2042 PMLR).)

Citation

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Cheng Mao. Ashwin Pananjady. Martin J. Wainwright. "Towards optimal estimation of bivariate isotonic matrices with unknown permutations." Ann. Statist. 48 (6) 3183 - 3205, December 2020. https://doi.org/10.1214/19-AOS1925

Information

Received: 1 June 2019; Revised: 1 November 2019; Published: December 2020
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185805
Digital Object Identifier: 10.1214/19-AOS1925

Subjects:
Primary: 62F07, 62J15

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 6 • December 2020
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