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Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial
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SYSNO ASEP 0475182 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial Tvůrce(i) Grim, Jiří (UTIA-B) RID, ORCID Celkový počet autorů 1 Číslo článku 1750028 Zdroj.dok. International Journal of Pattern Recognition and Artificial Intelligence - ISSN 0218-0014
Roč. 31, č. 9 (2017)Poč.str. 37 s. Forma vydání Online - E Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova multivariate statistics ; product mixtures ; naive Bayes models ; EM algorithm ; pattern recognition ; neural networks ; expert systems ; image analysis Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GA17-18407S GA ČR - Grantová agentura ČR Institucionální podpora UTIA-B - RVO:67985556 UT WOS 000402745500001 EID SCOPUS 85016474470 DOI https://doi.org/10.1142/S0218001417500288 Anotace In literature the references to EM estimation of product mixtures are not very frequent. The simplifying assumption of product components, e.g. diagonal covariance matrices in case of Gaussian mixtures, is usually considered only as a compromise because of some computational constraints or limited data set. We have found that the product mixtures are rarely used intentionally as a preferable approximating tool. Probably, most practitioners do not „trust“ the product components because of their formal similarity to „naive Bayes models“. Another reason could be an unrecognized numerical instability of EM algorithm in multidimensional spaces. In this paper we recall that the product mixture model does not imply the assumption of independence of variables. It is even not restrictive if the number of components is large enough. In addition, the product components increase numerical stability of the standard EM algorithm, simplify the EM iterations and have some other important advantages. We discuss and explain the implementation details of EM algorithm and summarize our experience in estimating product mixtures. Finally we illustrate the wide applicability of product mixtures in pattern recognition and in other fields. Pracoviště Ústav teorie informace a automatizace Kontakt Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Rok sběru 2018
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