Statistics – Computation
Scientific paper
2007-12-27
Journal of the Royal Statistical Society Series B (Statistical Methodology) 71, 3 (2009) 593-613
Statistics
Computation
Version that includes the corrigendum published in volume 73, part 5 (2011), of the Journal of the Royal Statistical Society,
Scientific paper
10.1111/j.1467-9868.2009.00698.x
In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the algorithm of Titterington (1984), this approach is more directly connected to the usual EM algorithm and does not rely on integration with respect to the complete data distribution. The resulting algorithm is usually simpler and is shown to achieve convergence to the stationary points of the Kullback-Leibler divergence between the marginal distribution of the observation and the model distribution at the optimal rate, i.e., that of the maximum likelihood estimator. In addition, the proposed approach is also suitable for conditional (or regression) models, as illustrated in the case of the mixture of linear regressions model.
Cappé Olivier
Moulines Eric
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