The expectation-maximization (EM) algorithm is a powerful
computational technique for locating maxima of functions. It is widely used in
statistics for maximum likelihood or maximum a posteriori estimation in
incomplete data models. In certain situations, however, this method is not
applicable because the expectation step cannot be performed in closed form. To
deal with these problems, a novel method is introduced, the stochastic
approximation EM (SAEM), which replaces the expectation step of the EM
algorithm by one iteration of a stochastic approximation procedure. The
convergence of the SAEM algorithm is established under conditions that are
applicable to many practical situations. Moreover, it is proved that, under
mild additional conditions, the attractive stationary points of the SAEM
algorithm correspond to the local maxima of the function presented to support
our findings.
Publié le : 1999-03-14
Classification:
Incomplete data,
optimization,
maximum likelihood,
missing data,
Monte Carlo algorithm,
EM algorithm,
simulation,
stochastic algorithm,
65U05,
62F10,
62M30,
60K35
@article{1018031103,
author = {Delyon, Bernard and Lavielle, Marc and Moulines, Eric},
title = {Convergence of a stochastic approximation version of the EM
algorithm},
journal = {Ann. Statist.},
volume = {27},
number = {4},
year = {1999},
pages = { 94-128},
language = {en},
url = {http://dml.mathdoc.fr/item/1018031103}
}
Delyon, Bernard; Lavielle, Marc; Moulines, Eric. Convergence of a stochastic approximation version of the EM
algorithm. Ann. Statist., Tome 27 (1999) no. 4, pp. 94-128. http://gdmltest.u-ga.fr/item/1018031103/