Tytuł:

Tight Lower Bound on Differential Entropy for Mixed Gaussian Distributions, Journal of Telecommunications and Information Technology, 2024, nr 2

Tytuł publikacji grupowej:

2024, nr 2, JTIT-artykuły

Autor:

Marconi, Abdelrahman ; Elghandour, Ahmed H. ; Elbayoumy, Ashraf D. ; Abdelaziz, Amr

Temat i słowa kluczowe:

differential entropy ; lower bound ; mixture random variable ; multimodal Gaussian

Abstrakt:

In this paper, a tight lower bound for the differential entropy of the Gaussian mixture model is presented. First, the probability model of mixed Gaussian distribution that is created by mixing both discrete and continuous random variables is investigated in order to represent symmetric bimodal Gaussian distribution using the hyperbolic cosine function, on which a tighter upper bound is set. Then, this tight upper bound is used to derive a tight lower bound for the differential entropy of the Gaussian mixture model introduced. The proposed lower bound allows to maintain its tightness over the entire range of the model's parameters and shows more tightness when compared with other bounds that lose their tightness over certain parameter ranges. The presented results are then extended to introduce a more general tight lower bound for asymmetric bimodal Gaussian distribution, in which the two modes have a symmetric mean but differ in terms of their weights.

Wydawca:

National Institute of Telecommunications

Data wydania:

2024

Typ zasobu:

artykuł

Identyfikator zasobu:

ISSN 1509-4553, on-line: ISSN 1899-8852

DOI:

10.26636/jtit.2024.2.1444

ISSN:

1509-4553

eISSN:

1899-8852

Źródło:

Journal of Telecommunications and Information Technology

Język:

ang

Licencja:

CC BY 4.0

Właściciel praw:

Instytut Łączności - Państwowy Instytut Badawczy