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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Shrnutí: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.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-020-09968-0