Minimax Risk Upper Bounds Based on Shell Analysis of a Quantized Maximum Likelihood Estimator

Noam Gavish*, Or Ordentlich

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This paper develops a unified framework for upper bounding the minimax risk in high-dimensional parameter estimation problems. To this end, we study a quantized maximum likelihood estimator, where the estimator computes the likelihood for all points within a discrete cover, and outputs the candidate with the maximal likelihood. While this concept is straightforward, our analysis is quite delicate. It splits the competing candidates in the cover to small shells, and controls the number of candidates in each shell, as well as the probability that a candidate in the shell outscores a candidate which is close to the true parameter. We demonstrate the utility of our bounds by applying them to different Gaussian problems, and showing that they recover the optimal minimax rate for the Gaussian location model and the spiked Wigner Model. For the multi-reference alignment problem we obtain a novel minimax upper bound, which essentially places no assumptions on the signal of interest.

Original languageAmerican English
Title of host publication2023 IEEE International Symposium on Information Theory, ISIT 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2105-2110
Number of pages6
ISBN (Electronic)9781665475549
DOIs
StatePublished - 2023
Event2023 IEEE International Symposium on Information Theory, ISIT 2023 - Taipei, Taiwan, Province of China
Duration: 25 Jun 202330 Jun 2023

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2023-June
ISSN (Print)2157-8095

Conference

Conference2023 IEEE International Symposium on Information Theory, ISIT 2023
Country/TerritoryTaiwan, Province of China
CityTaipei
Period25/06/2330/06/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Fingerprint

Dive into the research topics of 'Minimax Risk Upper Bounds Based on Shell Analysis of a Quantized Maximum Likelihood Estimator'. Together they form a unique fingerprint.

Cite this