Properties of the stochastic approximation EM algorithm with mini-batch sampling

To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation–Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classical conditions as the number of...

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Vydané v:	Statistics and computing Ročník 30; číslo 6; s. 1725 - 1739
Hlavní autori:	Kuhn, Estelle, Matias, Catherine, Rebafka, Tabea
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.11.2020 Springer Nature B.V Springer Verlag (Germany)
Predmet:	Algorithms Approximation Artificial Intelligence Computing time Convergence Markov chains Mathematical analysis Mathematics and Statistics Methodology Probability and Statistics in Computer Science Sampling Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs Statistics Theory Stochastic approximation Mini-batch sampling 62F12 65C60 EM algorithm Monte Carlo Markov chain stochastic approximation mini-batch sampling Monte Carlo Markov chain Mathematics Subject Classification 65C60 · 62F12
ISSN:	0960-3174, 1573-1375
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Abstract	To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation–Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classical conditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models. In particular, we highlight that mini-batch sampling results in an important speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented. Finally, we illustrate how to use mini-batch sampling in practice to improve results when a constraint on the computing time is given.
AbstractList	To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation–Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classical conditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models. In particular, we highlight that mini-batch sampling results in an important speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented. Finally, we illustrate how to use mini-batch sampling in practice to improve results when a constraint on the computing time is given. To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classicalconditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models.In particular, we highlight that mini-batch sampling results in an important speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented. Finally, we illustrate how to use mini-batch sampling in practice to improve results when a constraint on the computing time is given.
Author	Matias, Catherine Rebafka, Tabea Kuhn, Estelle
Author_xml	– sequence: 1 givenname: Estelle surname: Kuhn fullname: Kuhn, Estelle organization: MaIAGE, INRAE, Université Paris-Saclay – sequence: 2 givenname: Catherine surname: Matias fullname: Matias, Catherine organization: Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, Université de Paris, CNRS – sequence: 3 givenname: Tabea orcidid: 0000-0002-8998-7109 surname: Rebafka fullname: Rebafka, Tabea email: tabea.rebafka@upmc.fr organization: Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, Université de Paris, CNRS
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Cites_doi	10.1198/jcgs.2011.09109 10.1016/j.csda.2004.07.002 10.1111/j.1467-9868.2009.00698.x 10.1007/978-1-4757-4145-2 10.1111/j.1467-9868.2007.00574.x 10.1090/S0025-5718-2015-02952-4 10.1007/BF01908075 10.3150/09-BEJ229 10.1109/34.291440 10.1051/proc/201447004 10.1239/jap/1044476831 10.1007/s11222-019-09919-4 10.1137/S0363012902417267 10.1214/aos/1018031103 10.1051/ps:2004007 10.1111/j.2517-6161.1995.tb02037.x 10.1111/j.2517-6161.1984.tb01296.x 10.1111/j.2517-6161.1977.tb01600.x 10.3115/1620754.1620843
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References	Hubert, Arabie (CR12) 1985; 2 Cappé (CR4) 2011; 20 Lange (CR18) 1995; 2 Davidian, Giltinan (CR6) 1995 Duchateau, Janssen (CR9) 2008 Matias, Robin (CR20) 2014; 47 CR19 Andrieu, Moulines, Priouret (CR3) 2005; 44 CR16 Cappé, Moulines (CR5) 2009; 71 Dempster, Laird, Rubin (CR8) 1977; 39 CR15 Robert, Casella (CR23) 2004 CR14 Neal, Hinton, Jordan (CR21) 1999 Hull (CR13) 1994; 16 Fort, Jourdain, Kuhn, Lelièvre, Stoltz (CR11) 2015; 84 Fort, Moulines, Roberts, Rosenthal (CR10) 2003; 40 Kuhn, Lavielle (CR17) 2005; 49 Titterington (CR24) 1984; 2 Allassonnière, Kuhn, Trouvé (CR2) 2010; 16 Allassonnière, Amit, Trouvé (CR1) 2007; 69 Delyon, Lavielle, Moulines (CR7) 1999; 27 Nguyen, Forbes, McLachlan (CR22) 2020 L Hubert (9968_CR12) 1985; 2 S Allassonnière (9968_CR1) 2007; 69 AP Dempster (9968_CR8) 1977; 39 G Fort (9968_CR11) 2015; 84 C Matias (9968_CR20) 2014; 47 E Kuhn (9968_CR17) 2005; 49 9968_CR16 9968_CR15 RM Neal (9968_CR21) 1999 L Duchateau (9968_CR9) 2008 DM Titterington (9968_CR24) 1984; 2 9968_CR19 O Cappé (9968_CR5) 2009; 71 CP Robert (9968_CR23) 2004 H Nguyen (9968_CR22) 2020 O Cappé (9968_CR4) 2011; 20 9968_CR14 K Lange (9968_CR18) 1995; 2 JJ Hull (9968_CR13) 1994; 16 S Allassonnière (9968_CR2) 2010; 16 M Davidian (9968_CR6) 1995 G Fort (9968_CR10) 2003; 40 C Andrieu (9968_CR3) 2005; 44 B Delyon (9968_CR7) 1999; 27
References_xml	– volume: 20 start-page: 728 issue: 3 year: 2011 end-page: 749 ident: CR4 article-title: Online EM algorithm for hidden Markov models publication-title: J. Comput. Graph. Stat. doi: 10.1198/jcgs.2011.09109 – volume: 49 start-page: 1020 issue: 4 year: 2005 end-page: 1038 ident: CR17 article-title: Maximum likelihood estimation in nonlinear mixed effects models publication-title: Comput. Stat. Data Ann. doi: 10.1016/j.csda.2004.07.002 – volume: 71 start-page: 593 issue: 3 year: 2009 end-page: 613 ident: CR5 article-title: On-line expectation-maximization algorithm for latent data models publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.1467-9868.2009.00698.x – ident: CR19 – year: 2004 ident: CR23 publication-title: Monte Carlo statistical methods doi: 10.1007/978-1-4757-4145-2 – volume: 2 start-page: 257 issue: 46 year: 1984 end-page: 267 ident: CR24 article-title: Recursive parameter estimation using incomplete data publication-title: J. R. Stat. Soc. Ser. B – volume: 69 start-page: 3 year: 2007 end-page: 29 ident: CR1 article-title: Toward a coherent statistical framework for dense deformable template estimation publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.1467-9868.2007.00574.x – ident: CR14 – ident: CR15 – ident: CR16 – volume: 84 start-page: 2297 issue: 295 year: 2015 end-page: 2327 ident: CR11 article-title: Convergence of the Wang-Landau algorithm publication-title: Math. Comput. doi: 10.1090/S0025-5718-2015-02952-4 – volume: 2 start-page: 193 year: 1985 end-page: 218 ident: CR12 article-title: Comparing partitions publication-title: J. Classif. doi: 10.1007/BF01908075 – volume: 16 start-page: 641 issue: 3 year: 2010 end-page: 678 ident: CR2 article-title: Construction of Bayesian deformable models via a stochastic approximation algorithm: a convergence study publication-title: Bernoulli doi: 10.3150/09-BEJ229 – volume: 16 start-page: 550 issue: 5 year: 1994 end-page: 554 ident: CR13 article-title: A database for handwritten text recognition research publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.291440 – volume: 47 start-page: 55 year: 2014 end-page: 74 ident: CR20 article-title: Modeling heterogeneity in random graphs through latent space models: a selective review publication-title: ESAIM Proce. Surv. doi: 10.1051/proc/201447004 – volume: 39 start-page: 1 issue: 1 year: 1977 end-page: 38 ident: CR8 article-title: Maximum likelihood from incomplete data via the EM algorithm publication-title: J. R. Stat. Soc. Ser. B – start-page: 355 year: 1999 end-page: 368 ident: CR21 article-title: A view of the EM algorithm that justifies incremental, sparse, and other variants publication-title: Learning in Graphical Models – year: 2008 ident: CR9 publication-title: The Frailty Model – volume: 40 start-page: 123 year: 2003 end-page: 146 ident: CR10 article-title: On the geometric ergodicity of hybrid samplers publication-title: J. Appl. Probab. doi: 10.1239/jap/1044476831 – year: 2020 ident: CR22 publication-title: Mini-batch learning of exponential family finite mixture models doi: 10.1007/s11222-019-09919-4 – volume: 44 start-page: 283 issue: 1 year: 2005 end-page: 312 ident: CR3 article-title: Stability of stochastic approximation under verifiable conditions publication-title: SIAM J. Control. Optim. doi: 10.1137/S0363012902417267 – volume: 2 start-page: 425 issue: 57 year: 1995 end-page: 437 ident: CR18 article-title: A gradient algorithm locally equivalent to the EM algorithm publication-title: J. R. Stat. Soc. Ser. B – volume: 27 start-page: 94 issue: 1 year: 1999 end-page: 128 ident: CR7 article-title: Convergence of a stochastic approximation version of the EM algorithm publication-title: Ann. Stat. doi: 10.1214/aos/1018031103 – year: 1995 ident: CR6 publication-title: Nonlinear Models for Repeated Measurement Data – volume-title: Mini-batch learning of exponential family finite mixture models year: 2020 ident: 9968_CR22 doi: 10.1007/s11222-019-09919-4 – volume: 2 start-page: 193 year: 1985 ident: 9968_CR12 publication-title: J. Classif. doi: 10.1007/BF01908075 – volume: 27 start-page: 94 issue: 1 year: 1999 ident: 9968_CR7 publication-title: Ann. Stat. doi: 10.1214/aos/1018031103 – volume: 40 start-page: 123 year: 2003 ident: 9968_CR10 publication-title: J. Appl. Probab. doi: 10.1239/jap/1044476831 – ident: 9968_CR16 doi: 10.1051/ps:2004007 – volume: 16 start-page: 550 issue: 5 year: 1994 ident: 9968_CR13 publication-title: IEEE Trans. Pattern Anal. Mach. Intell. doi: 10.1109/34.291440 – volume: 69 start-page: 3 year: 2007 ident: 9968_CR1 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.1467-9868.2007.00574.x – volume: 2 start-page: 425 issue: 57 year: 1995 ident: 9968_CR18 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1995.tb02037.x – start-page: 355 volume-title: Learning in Graphical Models year: 1999 ident: 9968_CR21 – volume: 84 start-page: 2297 issue: 295 year: 2015 ident: 9968_CR11 publication-title: Math. Comput. doi: 10.1090/S0025-5718-2015-02952-4 – volume: 49 start-page: 1020 issue: 4 year: 2005 ident: 9968_CR17 publication-title: Comput. Stat. Data Ann. doi: 10.1016/j.csda.2004.07.002 – volume: 2 start-page: 257 issue: 46 year: 1984 ident: 9968_CR24 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1984.tb01296.x – volume-title: Monte Carlo statistical methods year: 2004 ident: 9968_CR23 doi: 10.1007/978-1-4757-4145-2 – volume: 71 start-page: 593 issue: 3 year: 2009 ident: 9968_CR5 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.1467-9868.2009.00698.x – volume: 16 start-page: 641 issue: 3 year: 2010 ident: 9968_CR2 publication-title: Bernoulli doi: 10.3150/09-BEJ229 – volume: 44 start-page: 283 issue: 1 year: 2005 ident: 9968_CR3 publication-title: SIAM J. Control. Optim. doi: 10.1137/S0363012902417267 – volume: 20 start-page: 728 issue: 3 year: 2011 ident: 9968_CR4 publication-title: J. Comput. Graph. Stat. doi: 10.1198/jcgs.2011.09109 – ident: 9968_CR14 – volume: 47 start-page: 55 year: 2014 ident: 9968_CR20 publication-title: ESAIM Proce. Surv. doi: 10.1051/proc/201447004 – ident: 9968_CR15 – volume-title: Nonlinear Models for Repeated Measurement Data year: 1995 ident: 9968_CR6 – volume: 39 start-page: 1 issue: 1 year: 1977 ident: 9968_CR8 publication-title: J. R. Stat. Soc. Ser. B doi: 10.1111/j.2517-6161.1977.tb01600.x – ident: 9968_CR19 doi: 10.3115/1620754.1620843 – volume-title: The Frailty Model year: 2008 ident: 9968_CR9
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Snippet	To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation–Maximization algorithm for general... To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general...
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SubjectTerms	Algorithms Approximation Artificial Intelligence Computing time Convergence Markov chains Mathematical analysis Mathematics and Statistics Methodology Probability and Statistics in Computer Science Sampling Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs Statistics Theory
Title	Properties of the stochastic approximation EM algorithm with mini-batch sampling
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