On the Ranking Recovery from Noisy Observations up to a Distortion

Document Type

Conference Proceeding

Publication Date

1-1-2022

Abstract

This paper considers the problem of recovering the ranking of a data vector from noisy observations, up to a distortion. Specifically, the noisy observations consist of the original data vector corrupted by isotropic additive Gaussian noise, and the distortion is measured in terms of a distance function between the estimated ranking and the true ranking of the original data vector. First, it is shown that an optimal (in terms of error probability) decision rule for the estimation task simply outputs the ranking of the noisy observation. Then, the error probability incurred by such a decision rule is characterized in the low-noise regime, and shown to grow sublinearly with the noise standard deviation. This result highlights that the proposed approximate version of the ranking recovery problem is significantly less noise-dominated than the exact recovery considered in [Jeong, ISIT 2021].

Identifier

85136302663 (Scopus)

ISBN

[9781665421591]

Publication Title

IEEE International Symposium on Information Theory Proceedings

External Full Text Location

https://doi.org/10.1109/ISIT50566.2022.9834780

ISSN

21578095

First Page

1993

Last Page

1998

Volume

2022-June

Grant

CCF-1849757

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS