Message passing expectation-maximization algorithms

Message passing algorithms have had dramatic impacts on important problems in signal processing, learning theory, communication theory, and information theory through their computational efficiency. Expectation-maximization algorithms have had dramatic impacts on problems in estimation and detection theory, but their computational efficiency often limits their applicability. Given a bipartite graphical model for the data, if a set of hidden independent random variables can be associated with the edges, then a resulting expectation-maximization algorithm is message passing on this graph. The algorithms are computationally efficient in the same sense as other message passing algorithms. One example of such algorithms is the standard expectation-maximization algorithm for emission tomography. Another example for a signal in Gaussian noise yields a statistical interpretation to efficient algorithms for sparse linear inverse problems.