
Dr. El Korso Mohammed Nabil, Laboratoire Energétique Mécanique Electromagnétisme (LEME), Université Paris Nanterre, France
Learning with the ExpectationMaximization Algorithm
The expectationmaximization approach is an iterative method that aims to find the
parameter of interest which maximizes the maximum likelihood objective function with a reduced
computational cost. Originally formulated in the seminal work of Arthur Dempster, Nan Laird, and
Donald Rubin in 1997, the EM is considered as one of the most fundamental contribution in the
statistic field that inspired many researchers. Since then, the EM has been the focus of enormous
theoretical advances and applications over the last nearly five decades, and continues to attract
much attention in both theoretical aspects and recent applications (e.g., biomedical, communication
systems for wireless communication, radar, sonar and array processing, etc.).
This tutorial will present, first, a mathematically understanding of the EM. Then, an
overview of some recent applications will be presented. Specifically, deep Gaussian mixture models
learning, structure learning, superimposed signals estimation and probabilistic robust sparse
principal component analysis will be considered. Finally, the tutorial ends with the presentation of
some recent accelerations and variants of the EM. Through the tutorial, several examples will
illustrate the interest of this technique for different signal processing applications such as robust
array processing, target classification and very large radio interferometer calibration.
