  It is shown how expectation maximization (EM) may be viewed as a message
passing algorithm in factor graphs. In particular, a general EM message
computation rule is identified. As a factor graph tool, EM may be used to break
cycles in a factor graph, and tractable messages may in some cases be obtained
where the sum-product messages are unwieldy.
  As an exemplary application, the paper considers linear Gaussian state space
models. Unknown coefficients in such models give rise to multipliers in the
corresponding factor graph. A main attraction of EM in such cases is that it
results in purely Gaussian message passing algorithms. These Gaussian EM
messages are tabulated for several (scalar, vector, matrix) multipliers that
frequently appear in applications.
