Various Performance Bounds on the Estimation of Low-Rank Probability Mass Function Tensors from Partial Observations

Tomer Hershkovitz*, Martin Haardt, Arie Yeredor*

*Corresponding author for this work

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

Abstract

Probability mass function (PMF) estimation using a low-rank model for the PMF tensor has gained increased popularity in recent years. However, its performance evaluation relied mostly on empirical testing. In this work, we derive theoretical bounds on the attainable performance under this model assumption. We begin by deriving the constrained Cramér-Rao Bound (CCRB) on the low-rank decomposition parameters, and then extend the CCRB to bounds on the mean square error in the resulting estimates of the PMF tensor's elements, as well as on the mean Kullback-Leibler divergence (KLD) between the estimated and true PMFs. The asymptotic tightness of these bounds is demonstrated by comparing them to the performance of the Maximum Likelihood estimate in a small-scale simulation example.

Original languageEnglish
Title of host publicationICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing, Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728163277
DOIs
StatePublished - 2023
Event48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023 - Rhodes Island, Greece
Duration: 4 Jun 202310 Jun 2023

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2023-June
ISSN (Print)1520-6149

Conference

Conference48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023
Country/TerritoryGreece
CityRhodes Island
Period4/06/2310/06/23

Funding

FundersFunder number
Deutsche ForschungsgemeinschaftHA 2239/16-1

    Keywords

    • Constrained Cramer-Rao Bound
    • KLD Bound
    • Low-Rank CPD
    • PMF Estimation

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