Optimizing the estimation of a histogram-bin width—application to the multivariate mixture-model estimation

Panić, Branislav (avtor), Klemenc, Jernej (avtor), Nagode, Marko (avtor)

A maximum-likelihood estimation of a multivariate mixture model's parameters is a difficult problem. One approach is to combine the REBMIX and EM algorithms. However, the REBMIX algorithm requires the use of histogram estimation, which is the most rudimentary approach to an empirical density estimation and has many drawbacks. Nevertheless, because of its simplicity, it is still one of the most commonly used techniques. The main problem is to estimate the optimum histogram-bin width, which is usually set by the number of non-overlapping, regularly spaced bins. For univariate problems it is usually denoted by an integer value; i.e., the number of bins. However, for multivariate problems, in order to obtain a histogram estimation, a regular grid must be formed. Thus, to obtain the optimum histogram estimation, an integer-optimization problem must be solved. The aim is therefore the estimation of optimum histogram binning, alone and in application to the mixture model parameter estimation with the REBMIX&EM strategy. As an estimator, the Knuth rule was used. For the optimization algorithm, a derivative based on the coordinate-descent optimization was composed. These proposals yielded promising results. The optimization algorithm was efficient and the results were accurate. When applied to the multivariate, Gaussian-mixture-model parameter estimation, the results were competitive. All the improvements were implemented in the rebmix R package.

• Jezik: Angleški jezik
• Ključne besede: histogram, integer optimization, parameter estimation, mixture model, EM, REBMIX
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FS - Fakulteta za strojništvo
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2020
• Št. strani: 30 str.
• Številčenje: Vol. 8, iss. 7, art. 1090
• PID: 20.500.12556/RUL-117438
• UDK: 004.4(045)
• ISSN pri članku: 2227-7390
• DOI: 10.3390/math8071090
• COBISS.SI-ID: 22207235
• Datum objave v RUL: 10.07.2020

PANIĆ, Branislav, KLEMENC, Jernej in NAGODE, Marko, 2020, Optimizing the estimation of a histogram-bin width—application to the multivariate mixture-model estimation. Mathematics [na spletu]. 2020. Vol. 8, no. 7,  1090. [Dostopano 4 maj 2025]. DOI 10.3390/math8071090. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=117438

Gradivo je del revije

• Naslov: Mathematics
• Skrajšan naslov: Mathematics
• Založnik: MDPI AG
• ISSN: 2227-7390
• COBISS.SI-ID: 523267865

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.
• Začetek licenciranja: 03.07.2020

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: histogram, diskretna optimizacija, ocena parametrov, EM, REBMIX, mešani model

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: 1000-18-0510