Maximum likelihood estimation for discrete latent variable models via evolutionary algorithms

We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic...

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Vydané v:	Statistics and computing Ročník 34; číslo 2
Hlavní autori:	Brusa, Luca, Pennoni, Fulvia, Bartolucci, Francesco
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.04.2024 Springer Nature B.V
Predmet:	Artificial Intelligence Computer Science Evolutionary algorithms Mathematical models Maxima Maximum likelihood estimation Monte Carlo simulation Original Paper Parameter estimation Probability and Statistics in Computer Science Statistical Theory and Methods Statistics and Computing/Statistics Programs Maximum-likelihood estimation Expectation–maximization algorithm Variational expectation–maximization algorithm Local maxima
ISSN:	0960-3174, 1573-1375
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Abstract	We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.
AbstractList	We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The proposal is based on modified versions of the expectation–maximization (EM) and variational EM (VEM) algorithms, which are based on the genetic approach and allow us to accurately explore the parameter space, reducing the chance to be trapped into one of the multiple local maxima of the log-likelihood function. Their performance is examined through an extensive Monte Carlo simulation study where they are employed to estimate latent class, hidden Markov, and stochastic block models and compared with the standard EM and VEM algorithms. We observe a significant increase in the chance to reach global maximum of the target function and a high accuracy of the estimated parameters for each model. Applications focused on the analysis of cross-sectional, longitudinal, and network data are proposed to illustrate and compare the algorithms.
ArticleNumber	62
Author	Bartolucci, Francesco Pennoni, Fulvia Brusa, Luca
Author_xml	– sequence: 1 givenname: Luca surname: Brusa fullname: Brusa, Luca email: luca.brusa@unimib.it organization: Department of Statistics and Quantitative Methods, University of Milano-Bicocca – sequence: 2 givenname: Fulvia surname: Pennoni fullname: Pennoni, Fulvia organization: Department of Statistics and Quantitative Methods, University of Milano-Bicocca – sequence: 3 givenname: Francesco surname: Bartolucci fullname: Bartolucci, Francesco organization: Department of Economics, University of Perugia
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Cites_doi	10.1016/j.patrec.2013.02.008 10.1093/oso/9780195099713.001.0001 10.1109/TIT.1967.1054010 10.1007/s11222-007-9046-7 10.1086/jar.33.4.3629752 10.1016/0378-8733(83)90021-7 10.1007/BF03372103 10.1080/10705510701575602 10.1198/016214501753208735 10.1109/TSMCC.2008.2007252 10.1007/s003579900004 10.1111/j.2517-6161.1964.tb00553.x 10.1109/34.865189 10.1093/biomet/61.2.215 10.1214/aoms/1177729694 10.1007/978-3-662-04131-4 10.1007/s11749-014-0381-7 10.1023/A:1007665907178 10.1214/aos/1176344136 10.1214/aoms/1177697196 10.1007/s00180-022-01276-7 10.1111/j.1467-985X.2006.00440.x 10.1111/j.2517-6161.1977.tb01600.x 10.1002/0471721182 10.1201/b20790 10.1007/s00357-020-09371-4 10.1080/01621459.1991.10475008 10.1109/TPAMI.2005.162 10.18637/jss.v081.i04 10.18637/jss.v053.i04 10.1111/insr.12436 10.1111/ecno.12193 10.1109/ICEC.1996.542329
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Snippet	We propose an evolutionary optimization method for maximum likelihood and approximate maximum likelihood estimation of discrete latent variable models. The...
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SubjectTerms	Artificial Intelligence Computer Science Evolutionary algorithms Mathematical models Maxima Maximum likelihood estimation Monte Carlo simulation Original Paper Parameter estimation Probability and Statistics in Computer Science Statistical Theory and Methods Statistics and Computing/Statistics Programs
Title	Maximum likelihood estimation for discrete latent variable models via evolutionary algorithms
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