I received an email question about the EM Algorithm. This is a computational approach that works well for missing data problems and data models with latent (unobserved) variabels. The basic approach is to estimate the missing or latent data (E-step), compute maximum likelihood estimates that incorporates the missing/latent estimates (M-step), then update the missing or latent data (E-step) and so forth. There's a book by McLachlan and Krishnan, The EM Algorithm and Extensions, that I have not seen, but which sounds pretty good. There are also a few good web sites about this algorithm.

**The Expectation Maximization Algorithm
[pdf]**. Dellaert F,
Georgia Institute of Technology. Accessed on 2004-03-15.
www.cc.gatech.edu/~dellaert/em-paper.pdf

**The EM Algorithm and its
Extensions**.
Bell Laboratories. Accessed on 2004-03-15.
cm.bell-labs.com/cm/ms/departments/sia/project/em/

**A Gentle Tutorial of the EM Algorithm and its Application to
Parameter Estimation for Gaussian Mixture and Hidden Markov Models
[pdf]**. Bilmes
JA, U.C. Berkeley. Accessed on 2004-03-15.
www.vision.ethz.ch/ml/slides/em_tutorial.pdf

If I get some time, I will show a simple example on my web pages.

You can find an earlier version of this page on my original website.