Learning Minimum Variance Unbiased Estimators

Tzvi Diskin, Yonina C. Eldar, Ami Wiesel

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

Abstract

The Gauss-Markov theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non-linear settings via deep learning with bias constraints. The classical approach to designing non-linear MVUEs is through maximum likelihood estimation (MLE) which often involves real-time computationally challenging optimizations. On the other hand, deep learning methods allow for non-linear estimators with fixed computational complexity. Learning based estimators perform optimally on average with respect to their training set but may suffer from significant bias in other parameters. To avoid this, we propose to add a simple bias constraint to the loss function, resulting in an estimator we refer to as Bias Constrained Estimator (BCE). We prove that this yields asymptotic MVUEs that behave similarly to the classical MLEs and asymptotically attain the Cramer Rao bound. We demonstrate the advantages of our approach in the context of signal to noise ratio estimation as well as covariance estimation.

Original languageAmerican English
Title of host publication2022 IEEE 12th Sensor Array and Multichannel Signal Processing Workshop, SAM 2022
PublisherIEEE Computer Society
Pages166-170
Number of pages5
ISBN (Electronic)9781665406338
DOIs
StatePublished - 2022
Event12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022 - Trondheim, Norway
Duration: 20 Jun 202223 Jun 2022

Publication series

NameProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
Volume2022-June
ISSN (Electronic)2151-870X

Conference

Conference12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022
Country/TerritoryNorway
CityTrondheim
Period20/06/2223/06/22

Bibliographical note

Publisher Copyright:
© 2022 IEEE.

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