Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F17%3A00475182" target="_blank" >RIV/67985556:_____/17:00475182 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1142/S0218001417500288" target="_blank" >http://dx.doi.org/10.1142/S0218001417500288</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218001417500288" target="_blank" >10.1142/S0218001417500288</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Approximation of Unknown Multivariate Probability Distributions by Using Mixtures of Product Components: A Tutorial

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

<a href="/cs/project/GA17-18407S" target="_blank" >GA17-18407S: Vizuálně optimalizované měření vzhledu materiálů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Pattern Recognition and Artificial Intelligence

ISSN

0218-0014

e-ISSN

—

Svazek periodika

31

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

37

Strana od-do

—

Kód UT WoS článku

000402745500001

EID výsledku v databázi Scopus

2-s2.0-85016474470