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

• Published in: Statistics and computing Vol. 30; no. 6; pp. 1725 - 1739
• Main Authors: Kuhn, Estelle, Matias, Catherine, Rebafka, Tabea
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2020; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: 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
• DOI: 10.1007/s11222-020-09968-0

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.