TY - GEN
T1 - Various Performance Bounds on the Estimation of Low-Rank Probability Mass Function Tensors from Partial Observations
AU - Hershkovitz, Tomer
AU - Haardt, Martin
AU - Yeredor, Arie
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
KW - Constrained Cramer-Rao Bound
KW - KLD Bound
KW - Low-Rank CPD
KW - PMF Estimation
UR - http://www.scopus.com/inward/record.url?scp=85177564599&partnerID=8YFLogxK
U2 - 10.1109/ICASSP49357.2023.10095206
DO - 10.1109/ICASSP49357.2023.10095206
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AN - SCOPUS:85177564599
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
BT - ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing, Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023
Y2 - 4 June 2023 through 10 June 2023
ER -