Frequentist parameter estimation with supervised learning

Year: 2021

Authors: Nolan SP., Pezzè L., Smerzi A.

Autors Affiliation: INO CNR, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy.

Abstract: Recently, there has been a great deal of interest surrounding the calibration of quantum sensors using machine learning techniques. This work explores the use of regression to infer a machine-learned point estimate of an unknown parameter. Although the analysis is necessarily frequentist-relying on repeated estimates to build up statistics-the authors clarify that this machine-learned estimator converges to the Bayesian maximum a posteriori estimator (subject to some regularity conditions). When the number of training measurements is large, this is identical to the well-known maximum-likelihood estimator (MLE), and using this fact, the authors argue that the Cramer-Rao sensitivity bound applies to the mean-square error cost function and can therefore be used to select optimal model and training parameters. The machine-learned estimator inherits the desirable asymptotic properties of the MLE, up to a limit imposed by the resolution of the training grid. Furthermore, the authors investigate the role of quantum noise in the training process and show that this noise imposes a fundamental limit on the number of grid points. This manuscript paves the way for machine-learning to assist the calibration of quantum sensors, thereby allowing maximum-likelihood inference to play a more prominent role in the design and operation of the next generation of ultra-precise sensors.

Journal/Review: AVS QUANTUM SCIENCE

Volume: 3 (3)      Pages from: 34401-1  to: 34401-12

More Information: We would like to thank V. Gebhart for useful discussions. We acknowledge financial support from the European Union’s Horizon 2020 research and innovation programme – Qombs Project, FET Flagship on Quantum Technologies grant no. 820419, and from the H2020 QuantERA ERA-NET Cofund in Quantum Technologies projects CEBBEC.
KeyWords: Permeation; Constant; Vacuum
DOI: 10.1116/5.0058163

Citations: 7
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-24
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